<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <title>Vector Algebra Breakdown: Triangle Midsegment</title>
  <style>
    * { box-sizing: border-box; margin: 0; padding: 0; }
    body {
      font-family: system-ui, -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
      background: #ffffff;
      color: #1e293b;
      padding: 10px;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      min-height: 100vh;
      max-height: 590px;
      overflow-x: hidden;
    }

    .container {
      width: 100%;
      max-width: 600px;
      display: flex;
      flex-direction: column;
      gap: 8px;
    }

    .main-grid {
      display: grid;
      grid-template-columns: 1.15fr 1fr;
      gap: 10px;
      width: 100%;
      align-items: stretch;
    }

    @media (max-width: 480px) {
      .main-grid {
        grid-template-columns: 1fr;
        gap: 8px;
      }
    }

    .svg-container {
      width: 100%;
      background: #f8fafc;
      border: 1px solid #e2e8f0;
      border-radius: 8px;
      padding: 6px;
      display: flex;
      justify-content: center;
      align-items: center;
      min-height: 190px;
    }

    svg {
      width: 100%;
      height: 100%;
      max-height: 200px;
      overflow: visible;
    }

    .steps-col {
      display: flex;
      flex-direction: column;
      gap: 6px;
      justify-content: center;
    }

    .step-card {
      background: #f8fafc;
      border: 1.5px solid #e2e8f0;
      border-radius: 8px;
      padding: 8px 10px;
      cursor: pointer;
      transition: border-color 0.2s, background-color 0.2s, box-shadow 0.2s;
      display: flex;
      flex-direction: column;
      gap: 2px;
    }

    .step-card:hover {
      background: #f1f5f9;
      border-color: #cbd5e1;
    }

    .step-card.active {
      background: #ffffff;
      border-color: #2563eb;
      box-shadow: 0 0 0 1px #2563eb, 0 2px 8px rgba(37,99,235,0.12);
    }

    .step-header {
      display: flex;
      align-items: center;
      justify-content: space-between;
    }

    .step-num {
      font-size: 11px;
      font-weight: 700;
      color: #64748b;
      text-transform: uppercase;
      letter-spacing: 0.5px;
    }

    .step-card.active .step-num {
      color: #2563eb;
    }

    .step-desc {
      font-size: 10.5px;
      color: #64748b;
    }

    /* Math formatting without external libraries */
    .math-eq {
      font-family: 'Cambria Math', 'Times New Roman', Georgia, serif;
      font-size: 13.5px;
      color: #0f172a;
      display: inline-flex;
      align-items: center;
      flex-wrap: wrap;
      gap: 3px;
      margin-top: 2px;
      line-height: 1.4;
    }

    .vec {
      display: inline-flex;
      flex-direction: column;
      align-items: center;
      line-height: 1;
      vertical-align: middle;
      padding: 0 1px;
    }

    .vec .arr {
      font-size: 9px;
      line-height: 0.7;
      color: inherit;
      user-select: none;
    }

    .vec .var {
      font-style: italic;
      font-weight: 600;
      font-size: 13px;
    }

    .frac {
      display: inline-flex;
      flex-direction: column;
      vertical-align: middle;
      text-align: center;
      font-size: 11px;
      line-height: 1;
      padding: 0 1.5px;
    }

    .frac .num {
      border-bottom: 1px solid currentColor;
      padding-bottom: 1px;
    }

    .frac .den {
      padding-top: 1px;
    }

    /* Conclusion Callout */
    .conclusion-bar {
      width: 100%;
      background: #eff6ff;
      border: 1px solid #bfdbfe;
      border-radius: 8px;
      padding: 8px 12px;
      display: flex;
      flex-wrap: wrap;
      align-items: center;
      justify-content: center;
      gap: 8px 16px;
      font-size: 12.5px;
      color: #1e3a8a;
    }

    .callout-item {
      display: flex;
      align-items: center;
      gap: 6px;
      white-space: nowrap;
    }

    .badge {
      display: inline-block;
      background: #2563eb;
      color: #ffffff;
      font-size: 10px;
      font-weight: 700;
      padding: 1px 6px;
      border-radius: 4px;
      text-transform: uppercase;
    }

    .callout-divider {
      color: #93c5fd;
      font-size: 14px;
    }

    @media (max-width: 480px) {
      .callout-divider {
        display: none;
      }
      .conclusion-bar {
        flex-direction: column;
        gap: 6px;
        align-items: flex-start;
      }
      .callout-item {
        white-space: normal;
      }
    }

    /* Controls */
    .controls {
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 10px;
      margin-top: 2px;
    }

    .btn {
      background: #f1f5f9;
      border: 1px solid #cbd5e1;
      border-radius: 6px;
      padding: 4px 10px;
      font-size: 12px;
      font-weight: 600;
      cursor: pointer;
      color: #334155;
      transition: background 0.15s;
    }

    .btn:hover {
      background: #e2e8f0;
    }

    .dots-container {
      display: flex;
      align-items: center;
      gap: 6px;
    }

    .dot {
      width: 8px;
      height: 8px;
      border-radius: 50%;
      background: #cbd5e1;
      cursor: pointer;
      transition: background-color 0.2s, opacity 0.2s;
    }

    .dot:hover {
      opacity: 0.8;
    }

    .dot.active {
      background: #2563eb;
      width: 10px;
      height: 10px;
    }

    /* SVG vector styling */
    .vec-line {
      stroke-linecap: round;
      transition: stroke 0.3s, stroke-width 0.3s, opacity 0.3s;
    }

    .vec-faint {
      opacity: 0.3;
      stroke-width: 1.8;
    }

    .vec-gold {
      stroke: #d97706;
      stroke-width: 3.2;
      opacity: 1;
    }

    .vec-blue {
      stroke: #2563eb;
      stroke-width: 3.2;
      opacity: 1;
    }

    .vec-purple {
      stroke: #7c3aed;
      stroke-width: 2.2;
    }

    .pt-lbl {
      font-size: 11px;
      font-weight: 700;
      fill: #1e293b;
      font-family: system-ui, sans-serif;
    }
  </style>
</head>
<body>

  <div class="container">
    <div class="main-grid">
      
      <div class="svg-container">
        <svg viewBox="0 0 250 190">
          <defs>
            <marker id="arr-slate" viewBox="0 0 10 10" refX="6" refY="5" markerWidth="5" markerHeight="5" orient="auto-start-reverse">
              <path d="M 0 1.5 L 8 5 L 0 8.5 z" fill="#64748b" />
            </marker>
            <marker id="arr-bc" viewBox="0 0 10 10" refX="6" refY="5" markerWidth="5" markerHeight="5" orient="auto-start-reverse">
              <path d="M 0 1.5 L 8 5 L 0 8.5 z" fill="#d97706" />
            </marker>
            <marker id="arr-mn" viewBox="0 0 10 10" refX="6" refY="5" markerWidth="5" markerHeight="5" orient="auto-start-reverse">
              <path d="M 0 1.5 L 8 5 L 0 8.5 z" fill="#2563eb" />
            </marker>
            <marker id="arr-purple" viewBox="0 0 10 10" refX="6" refY="5" markerWidth="5" markerHeight="5" orient="auto-start-reverse">
              <path d="M 0 1.5 L 8 5 L 0 8.5 z" fill="#7c3aed" />
            </marker>
          </defs>

          
          
          <line id="lineAB" x1="110" y1="22" x2="30" y2="155" stroke="#64748b" marker-end="url(#arr-slate)" class="vec-line" stroke-width="2" />
          
          <line id="lineAC" x1="110" y1="22" x2="220" y2="155" stroke="#64748b" marker-end="url(#arr-slate)" class="vec-line" stroke-width="2" />
          
          
          <line id="dashAM" x1="110" y1="22" x2="70" y2="88" stroke="#7c3aed" stroke-dasharray="3,3" stroke-width="2.5" marker-end="url(#arr-purple)" opacity="0" style="transition: opacity 0.3s;" />
          <line id="dashAN" x1="110" y1="22" x2="165" y2="88" stroke="#7c3aed" stroke-dasharray="3,3" stroke-width="2.5" marker-end="url(#arr-purple)" opacity="0" style="transition: opacity 0.3s;" />

          
          <line id="lineBC" x1="30" y1="155" x2="220" y2="155" stroke="#d97706" marker-end="url(#arr-bc)" class="vec-line vec-gold" />

          
          <line id="lineMN" x1="70" y1="88" x2="165" y2="88" stroke="#2563eb" marker-end="url(#arr-mn)" class="vec-line vec-faint" />

          
          <circle cx="110" cy="22" r="3.5" fill="#1e293b" />
          <text x="110" y="14" text-anchor="middle" class="pt-lbl">A</text>

          <circle cx="30" cy="155" r="3.5" fill="#1e293b" />
          <text x="18" y="162" class="pt-lbl">B</text>

          <circle cx="220" cy="155" r="3.5" fill="#1e293b" />
          <text x="228" y="162" class="pt-lbl">C</text>

          <circle cx="70" cy="88" r="3.5" fill="#2563eb" />
          <text x="54" y="88" class="pt-lbl">M</text>

          <circle cx="165" cy="88" r="3.5" fill="#2563eb" />
          <text x="174" y="88" class="pt-lbl">N</text>

          
          <text x="54" y="50" fill="#64748b" font-size="11" font-weight="600" font-style="italic">u</text>
          <text x="172" y="50" fill="#64748b" font-size="11" font-weight="600" font-style="italic">v</text>
          <text id="lblBC" x="125" y="174" text-anchor="middle" fill="#d97706" font-size="11.5" font-weight="700">BC = v − u</text>
          <text id="lblMN" x="118" y="80" text-anchor="middle" fill="#2563eb" font-size="11.5" font-weight="700">MN</text>
        </svg>
      </div>

      
      <div class="steps-col">
        
        <div class="step-card active" onclick="setStep(0)">
          <div class="step-header">
            <span class="step-num">Step 1</span>
            <span class="step-desc">Base Vector</span>
          </div>
          <div class="math-eq">
            <span class="vec"><span class="arr">→</span><span class="var">BC</span></span>
            <span>=</span>
            <span class="vec"><span class="arr">→</span><span class="var">v</span></span>
            <span>−</span>
            <span class="vec"><span class="arr">→</span><span class="var">u</span></span>
          </div>
        </div>

        
        <div class="step-card" onclick="setStep(1)">
          <div class="step-header">
            <span class="step-num">Step 2</span>
            <span class="step-desc">Midsegment</span>
          </div>
          <div class="math-eq">
            <span class="vec"><span class="arr">→</span><span class="var">MN</span></span>
            <span>=</span>
            <span class="frac"><span class="num">1</span><span class="den">2</span></span><span class="vec"><span class="arr">→</span><span class="var">v</span></span>
            <span>−</span>
            <span class="frac"><span class="num">1</span><span class="den">2</span></span><span class="vec"><span class="arr">→</span><span class="var">u</span></span>
          </div>
        </div>

        
        <div class="step-card" onclick="setStep(2)">
          <div class="step-header">
            <span class="step-num">Step 3</span>
            <span class="step-desc">Factor & Relate</span>
          </div>
          <div class="math-eq">
            <span class="vec"><span class="arr">→</span><span class="var">MN</span></span>
            <span>=</span>
            <span class="frac"><span class="num">1</span><span class="den">2</span></span>(<span class="vec"><span class="arr">→</span><span class="var">v</span></span> − <span class="vec"><span class="arr">→</span><span class="var">u</span></span>)
            <span>=</span>
            <span class="frac"><span class="num">1</span><span class="den">2</span></span><span class="vec"><span class="arr">→</span><span class="var">BC</span></span>
          </div>
        </div>
      </div>
    </div>

    
    <div class="conclusion-bar">
      <div class="callout-item" id="callout-parallel">
        <span class="badge">Parallel</span>
        <span><strong>MN ∥ BC</strong> (scalar k = ½ &gt; 0, same direction)</span>
      </div>
      <span class="callout-divider">•</span>
      <div class="callout-item" id="callout-length">
        <span class="badge">Magnitude</span>
        <span><strong>|MN| = ½|BC|</strong> (exactly half length)</span>
      </div>
    </div>

    
    <div class="controls">
      <button class="btn" id="playBtn" onclick="togglePlay()" aria-label="Pause or Play">⏸ Pause</button>
      <div class="dots-container">
        <div class="dot active" onclick="setStep(0)" title="Step 1"></div>
        <div class="dot" onclick="setStep(1)" title="Step 2"></div>
        <div class="dot" onclick="setStep(2)" title="Step 3"></div>
      </div>
    </div>
  </div>

  <script>
    let currentStep = 0;
    let playing = true;
    let timer = null;

    const cards = document.querySelectorAll(".step-card");
    const dots = document.querySelectorAll(".dot");
    const lineBC = document.getElementById("lineBC");
    const lineMN = document.getElementById("lineMN");
    const lineAB = document.getElementById("lineAB");
    const lineAC = document.getElementById("lineAC");
    const dashAM = document.getElementById("dashAM");
    const dashAN = document.getElementById("dashAN");
    const lblBC = document.getElementById("lblBC");
    const lblMN = document.getElementById("lblMN");
    const playBtn = document.getElementById("playBtn");

    function setStep(index) {
      currentStep = index;
      cards.forEach((c, i) => c.classList.toggle("active", i === index));
      dots.forEach((d, i) => d.classList.toggle("active", i === index));

      if (index === 0) {
        lineBC.setAttribute("class", "vec-line vec-gold");
        lineMN.setAttribute("class", "vec-line vec-faint");
        lineAB.setAttribute("class", "vec-line");
        lineAC.setAttribute("class", "vec-line");
        if (dashAM) dashAM.setAttribute("opacity", "0");
        if (dashAN) dashAN.setAttribute("opacity", "0");
        lblBC.textContent = "BC = v − u";
        lblMN.textContent = "MN";
      } else if (index === 1) {
        lineBC.setAttribute("class", "vec-line vec-faint");
        lineMN.setAttribute("class", "vec-line vec-blue");
        lineAB.setAttribute("class", "vec-line vec-faint");
        lineAC.setAttribute("class", "vec-line vec-faint");
        if (dashAM) dashAM.setAttribute("opacity", "1");
        if (dashAN) dashAN.setAttribute("opacity", "1");
        lblBC.textContent = "BC";
        lblMN.textContent = "MN = ½v − ½u";
      } else {
        lineBC.setAttribute("class", "vec-line vec-gold");
        lineMN.setAttribute("class", "vec-line vec-blue");
        lineAB.setAttribute("class", "vec-line vec-faint");
        lineAC.setAttribute("class", "vec-line vec-faint");
        if (dashAM) dashAM.setAttribute("opacity", "0.4");
        if (dashAN) dashAN.setAttribute("opacity", "0.4");
        lblBC.textContent = "BC";
        lblMN.textContent = "MN = ½ BC";
      }
    }

    function nextStep() {
      setStep((currentStep + 1) % 3);
    }

    function togglePlay() {
      playing = !playing;
      playBtn.textContent = playing ? "⏸ Pause" : "▶ Play";
      if (playing) {
        startTimer();
      } else {
        clearInterval(timer);
      }
    }

    function startTimer() {
      clearInterval(timer);
      timer = setInterval(nextStep, 3500);
    }

    setStep(0);
    startTimer();
  </script>
</body>
</html>

Vector Proofs of the Triangle Midsegment Theorem

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <meta name="aspect-ratio" content="1:1">
  <style>
    * { box-sizing: border-box; margin: 0; padding: 0; }
    body {
      font-family: system-ui, -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
      color: #1e2945;
      background: #ffffff;
      display: flex;
      flex-direction: column;
      align-items: center;
      padding: 8px;
      width: 100%;
      user-select: none;
    }

    .svg-wrap {
      width: 100%;
      max-width: 500px;
      position: relative;
    }

    svg {
      width: 100%;
      height: auto;
      display: block;
      overflow: visible;
    }

    .grid-line { stroke: #e2e8f0; stroke-width: 1; }
    .axis-line { stroke: #94a3b8; stroke-width: 1.5; }
    .axis-label { font-size: 11px; fill: #64748b; font-weight: 500; }

    .tri-side { stroke: #cbd5e1; stroke-width: 2; stroke-dasharray: 4 4; fill: none; }
    .tri-fill { fill: rgba(241, 245, 249, 0.5); }

    .vec-bc { stroke: #0f172a; stroke-width: 3.5; fill: none; }
    .vec-mn { stroke: #0284c7; stroke-width: 3.5; fill: none; }

    .delta-bc { stroke: #94a3b8; stroke-width: 1.5; stroke-dasharray: 3 3; fill: none; }
    .delta-mn { stroke: #38bdf8; stroke-width: 1.5; stroke-dasharray: 3 3; fill: none; }

    .pt-vtx { fill: #475569; }
    .pt-mid { fill: #f97316; filter: drop-shadow(0 0 4px rgba(249, 115, 22, 0.8)); }

    .pt-label { font-size: 12px; font-weight: 700; }
    .lbl-vtx { fill: #334155; }
    .lbl-mid { fill: #ea580c; }
    .lbl-mn { fill: #0284c7; font-size: 11px; font-weight: 600; }
    .lbl-bc { fill: #0f172a; font-size: 11px; font-weight: 600; }

    .card-grid {
      display: grid;
      grid-template-columns: 1fr 1fr;
      gap: 8px;
      width: 100%;
      max-width: 500px;
      margin-top: 8px;
    }

    .stat-card {
      border: 1.5px solid #e2e8f0;
      border-radius: 8px;
      padding: 6px 10px;
      background: #f8fafc;
      transition: box-shadow 0.2s, border-color 0.2s;
      cursor: pointer;
    }

    .stat-card.active-mn {
      border-color: #0284c7;
      background: #f0f9ff;
      box-shadow: 0 0 0 1px #0284c7;
    }

    .stat-card.active-bc {
      border-color: #0f172a;
      background: #f8fafc;
      box-shadow: 0 0 0 1px #0f172a;
    }

    .card-header {
      display: flex;
      align-items: center;
      justify-content: space-between;
      margin-bottom: 4px;
      font-size: 13px;
      font-weight: 700;
    }

    .badge-mn { color: #0284c7; }
    .badge-bc { color: #0f172a; }

    .row {
      display: flex;
      justify-content: space-between;
      font-size: 11px;
      line-height: 1.4;
      color: #475569;
    }

    .row span:last-child {
      font-weight: 600;
      font-family: ui-monospace, monospace;
      color: #0f172a;
    }

    .summary-bar {
      margin-top: 6px;
      width: 100%;
      max-width: 500px;
      background: #f1f5f9;
      border-radius: 6px;
      padding: 6px 12px;
      display: flex;
      align-items: center;
      justify-content: space-around;
      font-size: 12px;
      font-weight: 600;
    }

    .summary-item {
      display: flex;
      align-items: center;
      gap: 6px;
    }

    .tag {
      padding: 1px 6px;
      border-radius: 4px;
      font-size: 11px;
      font-weight: 700;
    }

    .tag-blue { background: #e0f2fe; color: #0369a1; }
    .tag-green { background: #dcfce7; color: #15803d; }
  </style>
</head>
<body>

  <div class="svg-wrap">
    <svg viewBox="0 0 540 450">
      <defs>
        
        <marker id="arrow-mn" viewBox="0 0 10 10" refX="7" refY="5" markerWidth="6" markerHeight="6" orient="auto-start-reverse">
          <path d="M 0 1.5 L 8 5 L 0 8.5 z" fill="#0284c7" />
        </marker>
        
        <marker id="arrow-bc" viewBox="0 0 10 10" refX="7" refY="5" markerWidth="6" markerHeight="6" orient="auto-start-reverse">
          <path d="M 0 1.5 L 8 5 L 0 8.5 z" fill="#0f172a" />
        </marker>
      </defs>

      
      
      <g>
        <line x1="35" y1="15" x2="35" y2="415" class="grid-line" />
        <line x1="75" y1="15" x2="75" y2="415" class="grid-line" />
        <line x1="115" y1="15" x2="115" y2="415" class="grid-line" />
        <line x1="155" y1="15" x2="155" y2="415" class="grid-line" />
        <line x1="195" y1="15" x2="195" y2="415" class="grid-line" />
        <line x1="235" y1="15" x2="235" y2="415" class="grid-line" />
        <line x1="275" y1="15" x2="275" y2="415" class="grid-line" />
        <line x1="315" y1="15" x2="315" y2="415" class="grid-line" />
        <line x1="355" y1="15" x2="355" y2="415" class="grid-line" />
        <line x1="395" y1="15" x2="395" y2="415" class="grid-line" />
        <line x1="435" y1="15" x2="435" y2="415" class="grid-line" />
        <line x1="475" y1="15" x2="475" y2="415" class="grid-line" />
        <line x1="515" y1="15" x2="515" y2="415" class="grid-line" />
      </g>

      
      <g>
        <line x1="35" y1="415" x2="515" y2="415" class="grid-line" />
        <line x1="35" y1="375" x2="515" y2="375" class="grid-line" />
        <line x1="35" y1="335" x2="515" y2="335" class="grid-line" />
        <line x1="35" y1="295" x2="515" y2="295" class="grid-line" />
        <line x1="35" y1="255" x2="515" y2="255" class="grid-line" />
        <line x1="35" y1="215" x2="515" y2="215" class="grid-line" />
        <line x1="35" y1="175" x2="515" y2="175" class="grid-line" />
        <line x1="35" y1="135" x2="515" y2="135" class="grid-line" />
        <line x1="35" y1="95" x2="515" y2="95" class="grid-line" />
        <line x1="35" y1="55" x2="515" y2="55" class="grid-line" />
        <line x1="35" y1="15" x2="515" y2="15" class="grid-line" />
      </g>

      
      <line x1="35" y1="415" x2="525" y2="415" class="axis-line" />
      <line x1="35" y1="415" x2="35" y2="8" class="axis-line" />

      
      <g text-anchor="middle" class="axis-label">
        <text x="35" y="430">0</text>
        <text x="115" y="430">2</text>
        <text x="195" y="430">4</text>
        <text x="275" y="430">6</text>
        <text x="355" y="430">8</text>
        <text x="435" y="430">10</text>
        <text x="515" y="430">12</text>
        <text x="532" y="419" font-weight="700">x</text>
      </g>

      <g text-anchor="end" class="axis-label">
        <text x="28" y="339">2</text>
        <text x="28" y="259">4</text>
        <text x="28" y="179">6</text>
        <text x="28" y="99">8</text>
        <text x="28" y="19">10</text>
        <text x="32" y="10" font-weight="700" text-anchor="middle">y</text>
      </g>

      
      
      <polygon points="35,415 195,95 435,335" class="tri-fill" />
      <line x1="35" y1="415" x2="195" y2="95" class="tri-side" />
      <line x1="35" y1="415" x2="435" y2="335" class="tri-side" />

      
      
      <g id="delta-bc-group">
        <polyline points="195,95 435,95 435,335" class="delta-bc" />
        <text x="315" y="87" text-anchor="middle" class="lbl-bc">dx = +6</text>
        <text x="443" y="220" text-anchor="start" class="lbl-bc">dy = -6</text>
      </g>

      
      
      <g id="delta-mn-group">
        <polyline points="115,255 235,255 235,375" class="delta-mn" />
        <text x="175" y="247" text-anchor="middle" class="lbl-mn">dx = +3</text>
        <text x="243" y="320" text-anchor="start" class="lbl-mn">dy = -3</text>
      </g>

      
      <line x1="195" y1="95" x2="431" y2="331" class="vec-bc" marker-end="url(#arrow-bc)" />

      
      <line x1="115" y1="255" x2="231" y2="371" class="vec-mn" marker-end="url(#arrow-mn)" />

      
      <circle cx="35" cy="415" r="4.5" class="pt-vtx" />
      <text x="47" y="410" class="pt-label lbl-vtx">A(0,0)</text>

      <circle cx="195" cy="95" r="4.5" class="pt-vtx" />
      <text x="195" y="80" text-anchor="middle" class="pt-label lbl-vtx">B(4,8)</text>

      <circle cx="435" cy="335" r="4.5" class="pt-vtx" />
      <text x="447" y="352" class="pt-label lbl-vtx">C(10,2)</text>

      
      <circle cx="115" cy="255" r="6" class="pt-mid" />
      <text x="98" y="250" text-anchor="end" class="pt-label lbl-mid">M(2,4)</text>

      <circle cx="235" cy="375" r="6" class="pt-mid" />
      <text x="220" y="398" text-anchor="end" class="pt-label lbl-mid">N(5,1)</text>

      
      <text x="160" y="328" class="lbl-mn" font-weight="700">MN</text>
      <text x="330" y="200" class="lbl-bc" font-weight="700">BC</text>
    </svg>
  </div>

  
  <div class="card-grid">
    
    <div class="stat-card active-mn" id="cardMN">
      <div class="card-header badge-mn">
        <span>Vector MN</span>
        <span>(3, -3)</span>
      </div>
      <div class="row">
        <span>Slope (dy/dx)</span>
        <span>-3 / 3 = -1</span>
      </div>
      <div class="row">
        <span>Length |MN|</span>
        <span>3√2 ≈ 4.24</span>
      </div>
    </div>

    
    <div class="stat-card active-bc" id="cardBC">
      <div class="card-header badge-bc">
        <span>Vector BC</span>
        <span>(6, -6)</span>
      </div>
      <div class="row">
        <span>Slope (dy/dx)</span>
        <span>-6 / 6 = -1</span>
      </div>
      <div class="row">
        <span>Length |BC|</span>
        <span>6√2 ≈ 8.49</span>
      </div>
    </div>
  </div>

  
  <div class="summary-bar">
    <div class="summary-item">
      <span>Parallel:</span>
      <span class="tag tag-blue">m₁ = m₂ = -1</span>
    </div>
    <div class="summary-item">
      <span>Scale:</span>
      <span class="tag tag-green">|BC| = 2 · |MN|</span>
    </div>
  </div>

  <script>
    const cardMN = document.getElementById('cardMN');
    const cardBC = document.getElementById('cardBC');
    const deltaMN = document.getElementById('delta-mn-group');
    const deltaBC = document.getElementById('delta-bc-group');

    let mnVisible = true;
    let bcVisible = true;

    cardMN.addEventListener('click', () => {
      mnVisible = !mnVisible;
      deltaMN.style.opacity = mnVisible ? '1' : '0.15';
      cardMN.style.opacity = mnVisible ? '1' : '0.5';
    });

    cardBC.addEventListener('click', () => {
      bcVisible = !bcVisible;
      deltaBC.style.opacity = bcVisible ? '1' : '0.15';
      cardBC.style.opacity = bcVisible ? '1' : '0.5';
    });
  </script>
</body>
</html>

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <meta name="aspect-ratio" content="1:1">
  <style>
    * { box-sizing: border-box; margin: 0; padding: 0; }
    body {
      font-family: system-ui, -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
      color: #1e2945;
      background: #ffffff;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: space-between;
      width: 100%;
      height: 100%;
      padding: 10px 12px;
      user-select: none;
      -webkit-user-select: none;
    }

    .toolbar {
      display: flex;
      gap: 6px;
      width: 100%;
      max-width: 360px;
      justify-content: center;
    }

    .step-btn {
      flex: 1;
      padding: 6px 4px;
      font-size: 13px;
      font-weight: 600;
      border: 1px solid #e2e8f0;
      background: #f8fafc;
      color: #64748b;
      border-radius: 8px;
      cursor: pointer;
      text-align: center;
      transition: all 0.2s ease;
    }

    .step-btn.active {
      background: #eff6ff;
      color: #2563eb;
      border-color: #93c5fd;
      box-shadow: 0 1px 3px rgba(37, 99, 235, 0.12);
    }

    .svg-container {
      width: 100%;
      max-width: 360px;
      flex: 1;
      display: flex;
      align-items: center;
      justify-content: center;
      min-height: 220px;
    }

    svg {
      width: 100%;
      height: 100%;
      overflow: visible;
    }

    .formula-card {
      width: 100%;
      max-width: 360px;
      background: #f8fafc;
      border: 1px solid #e2e8f0;
      border-radius: 10px;
      padding: 8px 12px;
      text-align: center;
      font-size: 15px;
      font-weight: 600;
      min-height: 48px;
      display: flex;
      align-items: center;
      justify-content: center;
      box-shadow: 0 1px 2px rgba(0,0,0,0.04);
    }

    .vector-u { color: #2563eb; }
    .vector-v { color: #9333ea; }
    .vector-base { color: #475569; }
    .vector-mn { color: #059669; }

    .fade-item {
      transition: opacity 0.3s ease, stroke-dashoffset 0.3s ease;
    }
  </style>
</head>
<body>

  <div class="toolbar">
    <button class="step-btn active" id="btn0" onclick="setStep(0)">1. Sides</button>
    <button class="step-btn" id="btn1" onclick="setStep(1)">2. Midpoints</button>
    <button class="step-btn" id="btn2" onclick="setStep(2)">3. Vector Path</button>
    <button class="step-btn" id="btn3" onclick="setStep(3)">4. Midsegment</button>
  </div>

  <div class="svg-container">
    <svg viewBox="0 0 360 260">
      <defs>
        
        <marker id="arrow-blue" viewBox="0 0 10 10" refX="8" refY="5" markerWidth="6" markerHeight="6" orient="auto">
          <path d="M 0 1 L 10 5 L 0 9 z" fill="#2563eb" />
        </marker>
        <marker id="arrow-purple" viewBox="0 0 10 10" refX="8" refY="5" markerWidth="6" markerHeight="6" orient="auto">
          <path d="M 0 1 L 10 5 L 0 9 z" fill="#9333ea" />
        </marker>
        <marker id="arrow-gray" viewBox="0 0 10 10" refX="8" refY="5" markerWidth="6" markerHeight="6" orient="auto">
          <path d="M 0 1 L 10 5 L 0 9 z" fill="#64748b" />
        </marker>
        <marker id="arrow-green" viewBox="0 0 10 10" refX="8" refY="5" markerWidth="6" markerHeight="6" orient="auto">
          <path d="M 0 1 L 10 5 L 0 9 z" fill="#059669" />
        </marker>
        <marker id="arrow-amber" viewBox="0 0 10 10" refX="8" refY="5" markerWidth="6" markerHeight="6" orient="auto">
          <path d="M 0 1 L 10 5 L 0 9 z" fill="#d97706" />
        </marker>
      </defs>

      
      <polygon points="100,45 40,225 320,225" fill="#f1f5f9" opacity="0.6"/>

      
      <line x1="100" y1="45" x2="43" y2="216" stroke="#2563eb" stroke-width="2.5" marker-end="url(#arrow-blue)" />
      
      
      <line x1="100" y1="45" x2="313" y2="219" stroke="#9333ea" stroke-width="2.5" marker-end="url(#arrow-purple)" />
      
      
      <line x1="40" y1="225" x2="310" y2="225" stroke="#64748b" stroke-width="2.5" marker-end="url(#arrow-gray)" />

      
      <g id="midpoint-group" class="fade-item" opacity="0">
        
        <line x1="64" y1="87" x2="76" y2="92" stroke="#2563eb" stroke-width="2" stroke-linecap="round" />
        
        <line x1="49" y1="177" x2="61" y2="182" stroke="#2563eb" stroke-width="2" stroke-linecap="round" />
        
        <line x1="149" y1="88" x2="161" y2="98" stroke="#9333ea" stroke-width="1.8" stroke-linecap="round" />
        <line x1="154" y1="84" x2="166" y2="94" stroke="#9333ea" stroke-width="1.8" stroke-linecap="round" />
        
        <line x1="259" y1="178" x2="271" y2="188" stroke="#9333ea" stroke-width="1.8" stroke-linecap="round" />
        <line x1="264" y1="174" x2="276" y2="184" stroke="#9333ea" stroke-width="1.8" stroke-linecap="round" />

        
        <circle cx="70" cy="135" r="5" fill="#059669" />
        <text x="50" y="139" font-size="14" font-weight="700" fill="#059669">M</text>

        <circle cx="210" cy="135" r="5" fill="#059669" />
        <text x="220" y="139" font-size="14" font-weight="700" fill="#059669">N</text>
      </g>

      
      <g id="path-group" class="fade-item" opacity="0">
        <line x1="70" y1="135" x2="97" y2="54" stroke="#d97706" stroke-width="3" stroke-dasharray="4,4" marker-end="url(#arrow-amber)" />
        <line x1="100" y1="45" x2="204" y2="130" stroke="#d97706" stroke-width="3" stroke-dasharray="4,4" marker-end="url(#arrow-amber)" />
        <text x="68" y="78" font-size="12" font-weight="700" fill="#d97706">−½u</text>
        <text x="162" y="80" font-size="12" font-weight="700" fill="#d97706">+½v</text>
      </g>

      
      <g id="mn-group" class="fade-item" opacity="0">
        <line x1="70" y1="135" x2="202" y2="135" stroke="#059669" stroke-width="3" stroke-dasharray="5,4" marker-end="url(#arrow-green)" />
        <text x="122" y="125" font-size="14" font-weight="700" fill="#059669">MN</text>
      </g>

      
      <text x="96" y="32" font-size="15" font-weight="700" fill="#1e2945">A</text>
      <text x="22" y="235" font-size="15" font-weight="700" fill="#1e2945">B</text>
      <text x="328" y="235" font-size="15" font-weight="700" fill="#1e2945">C</text>

      
      <text x="50" y="105" font-size="14" font-weight="700" fill="#2563eb">u</text>
      <text x="215" y="105" font-size="14" font-weight="700" fill="#9333ea">v</text>
      <text x="155" y="248" font-size="14" font-weight="700" fill="#475569">v − u</text>
    </svg>
  </div>

  <div class="formula-card" id="formulaBox">
    <span>Base: <b class="vector-base">BC = v − u</b></span>
  </div>

  <script>
    const formulas = [
      '<span>Base vector: <b class="vector-base">BC = v − u</b></span>',
      '<span>Midpoints: <b class="vector-u">AM = ½u</b>, <b class="vector-v">AN = ½v</b></span>',
      '<span>Vector path: <b class="vector-mn">MN</b> = <b class="vector-u">−½u</b> + <b class="vector-v">½v</b></span>',
      '<span>Result: <b class="vector-mn">MN = ½(v − u) = ½BC</b> (parallel &amp; half length)</span>'
    ];

    let curStep = 0;

    function setStep(step) {
      curStep = step;
      for (let i = 0; i < 4; i++) {
        document.getElementById('btn' + i).classList.toggle('active', i === step);
      }
      
      const midpoints = document.getElementById('midpoint-group');
      const pathGroup = document.getElementById('path-group');
      const mnGroup = document.getElementById('mn-group');
      const formulaBox = document.getElementById('formulaBox');

      midpoints.setAttribute('opacity', step >= 1 ? '1' : '0');
      pathGroup.setAttribute('opacity', step === 2 ? '1' : '0');
      mnGroup.setAttribute('opacity', step >= 2 ? '1' : '0');
      
      formulaBox.innerHTML = formulas[step];
    }
  </script>
</body>
</html>

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <meta name="aspect-ratio" content="1:1">
  <title>Vector Equivalence and Standard Position</title>
  <style>
    * {
      box-sizing: border-box;
      margin: 0;
      padding: 0;
      font-family: system-ui, -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
    }

    body {
      background: #ffffff;
      color: #1e2945;
      display: flex;
      flex-direction: column;
      align-items: center;
      padding: 12px;
      gap: 10px;
      width: 100%;
      user-select: none;
    }

    /* Controls */
    .controls {
      display: flex;
      flex-wrap: wrap;
      gap: 8px;
      justify-content: center;
      width: 100%;
      max-width: 480px;
    }

    .btn-step {
      background: #f8fafc;
      border: 1px solid #cbd5e1;
      color: #475569;
      font-size: 13px;
      font-weight: 600;
      padding: 6px 14px;
      border-radius: 20px;
      cursor: pointer;
      transition: all 0.2s ease;
      display: inline-flex;
      align-items: center;
      gap: 6px;
    }

    .btn-step:hover {
      background: #f1f5f9;
      color: #1e2945;
    }

    .btn-step.active {
      background: #2563eb;
      border-color: #2563eb;
      color: #ffffff;
      box-shadow: 0 2px 6px rgba(37, 99, 235, 0.25);
    }

    /* SVG Plane */
    .grid-container {
      width: 100%;
      max-width: 440px;
      aspect-ratio: 1 / 1;
      position: relative;
    }

    svg {
      width: 100%;
      height: 100%;
      overflow: visible;
    }

    .grid-line {
      stroke: #e2e8f0;
      stroke-width: 1;
    }

    .axis-line {
      stroke: #64748b;
      stroke-width: 1.5;
    }

    .axis-tick-label {
      font-size: 11px;
      fill: #64748b;
      font-weight: 500;
      text-anchor: middle;
      dominant-baseline: middle;
    }

    /* Vectors & Components */
    .vec-v {
      stroke: #2563eb;
      stroke-width: 3.5;
      stroke-linecap: round;
    }

    .vec-ab {
      stroke: #7c3aed;
      stroke-width: 3.5;
      stroke-linecap: round;
    }

    .comp-dx {
      stroke: #ea580c;
      stroke-width: 2;
      stroke-dasharray: 4, 3;
    }

    .comp-dy {
      stroke: #16a34a;
      stroke-width: 2;
      stroke-dasharray: 4, 3;
    }

    .label-tag {
      font-size: 11px;
      font-weight: 700;
      text-anchor: middle;
      dominant-baseline: central;
    }

    /* Animated Vector Group */
    #group-ab {
      transition: transform 0.6s cubic-bezier(0.4, 0, 0.2, 1), opacity 0.4s ease;
    }

    #group-v {
      transition: opacity 0.4s ease;
    }

    .helper-group {
      transition: opacity 0.3s ease;
    }

    /* Formula Banner */
    .formula-panel {
      width: 100%;
      max-width: 440px;
      background: #f8fafc;
      border: 1px solid #e2e8f0;
      border-radius: 8px;
      padding: 8px 12px;
      text-align: center;
      min-height: 48px;
      display: flex;
      flex-direction: column;
      justify-content: center;
      align-items: center;
      gap: 3px;
    }

    .formula-math {
      font-size: 14px;
      font-weight: 700;
      color: #1e2945;
      letter-spacing: 0.2px;
    }

    .formula-desc {
      font-size: 12px;
      color: #64748b;
      font-weight: 500;
    }

    .hl-blue { color: #2563eb; }
    .hl-purple { color: #7c3aed; }
    .hl-orange { color: #ea580c; }
    .hl-green { color: #16a34a; }
  </style>
</head>
<body>

  
  <div class="controls">
    <button class="btn-step active" id="btn-0" onclick="setStep(0)">1. Components</button>
    <button class="btn-step" id="btn-1" onclick="setStep(1)">2. Slide &amp; Overlay</button>
    <button class="btn-step" id="btn-2" onclick="setStep(2)">3. Standard Position</button>
  </div>

  
  <div class="grid-container">
    <svg viewBox="0 0 380 380" id="plot">
      <defs>
        
        <marker id="arrow-v" viewBox="0 0 10 10" refX="7" refY="5" markerWidth="6" markerHeight="6" orient="auto-start-reverse">
          <path d="M 0 1.5 L 8 5 L 0 8.5 z" fill="#2563eb" />
        </marker>
        
        <marker id="arrow-ab" viewBox="0 0 10 10" refX="7" refY="5" markerWidth="6" markerHeight="6" orient="auto-start-reverse">
          <path d="M 0 1.5 L 8 5 L 0 8.5 z" fill="#7c3aed" />
        </marker>
      </defs>

      
      
      <g>
        
        <line x1="40" y1="290" x2="340" y2="290" class="grid-line" />
        <line x1="40" y1="240" x2="340" y2="240" class="grid-line" />
        <line x1="40" y1="190" x2="340" y2="190" class="grid-line" />
        <line x1="40" y1="140" x2="340" y2="140" class="grid-line" />
        <line x1="40" y1="90"  x2="340" y2="90"  class="grid-line" />
        <line x1="40" y1="40"  x2="340" y2="40"  class="grid-line" />
        
        <line x1="90"  y1="40" x2="90"  y2="340" class="grid-line" />
        <line x1="140" y1="40" x2="140" y2="340" class="grid-line" />
        <line x1="190" y1="40" x2="190" y2="340" class="grid-line" />
        <line x1="240" y1="40" x2="240" y2="340" class="grid-line" />
        <line x1="290" y1="40" x2="290" y2="340" class="grid-line" />
        <line x1="340" y1="40" x2="340" y2="340" class="grid-line" />

        
        <line x1="40" y1="340" x2="355" y2="340" class="axis-line" marker-end="url(#arrow-axis)" />
        <line x1="40" y1="340" x2="40" y2="25" class="axis-line" marker-end="url(#arrow-axis)" />

        
        <text x="365" y="340" class="axis-tick-label" font-weight="700">x</text>
        <text x="40" y="15" class="axis-tick-label" font-weight="700">y</text>

        
        <text x="40"  y="355" class="axis-tick-label">0</text>
        <text x="90"  y="355" class="axis-tick-label">1</text>
        <text x="140" y="355" class="axis-tick-label">2</text>
        <text x="190" y="355" class="axis-tick-label">3</text>
        <text x="240" y="355" class="axis-tick-label">4</text>
        <text x="290" y="355" class="axis-tick-label">5</text>
        <text x="340" y="355" class="axis-tick-label">6</text>

        
        <text x="25" y="290" class="axis-tick-label">1</text>
        <text x="25" y="240" class="axis-tick-label">2</text>
        <text x="25" y="190" class="axis-tick-label">3</text>
        <text x="25" y="140" class="axis-tick-label">4</text>
        <text x="25" y="90"  class="axis-tick-label">5</text>
        <text x="25" y="40"  class="axis-tick-label">6</text>
      </g>

      
      <g id="group-v">
        
        <g id="helpers-v" class="helper-group">
          <line x1="40" y1="340" x2="190" y2="340" class="comp-dx" />
          <line x1="190" y1="340" x2="190" y2="140" class="comp-dy" />
          <rect x="95" y="343" width="40" height="15" rx="3" fill="#fff" opacity="0.9"/>
          <text x="115" y="351" class="label-tag" fill="#ea580c">Δx = 3</text>
          <rect x="193" y="233" width="40" height="15" rx="3" fill="#fff" opacity="0.9"/>
          <text x="213" y="241" class="label-tag" fill="#16a34a">Δy = 4</text>
        </g>

        
        <line x1="40" y1="340" x2="190" y2="140" class="vec-v" marker-end="url(#arrow-v)" />
        <circle cx="40" cy="340" r="4.5" fill="#2563eb" />
        <circle cx="190" cy="140" r="3.5" fill="#2563eb" />

        
        <rect x="90" y="222" width="62" height="20" rx="10" fill="#2563eb" />
        <text x="121" y="232" class="label-tag" fill="#ffffff">v = ⟨3, 4⟩</text>

        <g id="standard-tag" opacity="0">
          <rect x="42" y="322" width="68" height="14" rx="3" fill="#eff6ff" stroke="#2563eb" stroke-width="1"/>
          <text x="76" y="329" class="label-tag" fill="#2563eb" font-size="9.5">Tail at Origin</text>
          <text x="190" y="125" class="label-tag" fill="#2563eb" font-size="11">Terminal (3,4)</text>
        </g>
      </g>

      
      <g id="group-ab">
        
        <g id="helpers-ab" class="helper-group">
          <line x1="90" y1="290" x2="240" y2="290" class="comp-dx" />
          <line x1="240" y1="290" x2="240" y2="90" class="comp-dy" />
          <rect x="142" y="293" width="46" height="15" rx="3" fill="#fff" opacity="0.9"/>
          <text x="165" y="301" class="label-tag" fill="#ea580c">Δx = +3</text>
          <rect x="243" y="182" width="46" height="15" rx="3" fill="#fff" opacity="0.9"/>
          <text x="266" y="190" class="label-tag" fill="#16a34a">Δy = +4</text>
        </g>

        
        <line x1="90" y1="290" x2="240" y2="90" class="vec-ab" marker-end="url(#arrow-ab)" />
        <circle cx="90" cy="290" r="4.5" fill="#7c3aed" />
        <circle cx="240" cy="90" r="3.5" fill="#7c3aed" />

        
        <text x="78" y="280" class="label-tag" fill="#7c3aed" id="label-pt-a">A(1,1)</text>
        <text x="252" y="80" class="label-tag" fill="#7c3aed" id="label-pt-b">B(4,5)</text>

        
        <rect x="162" y="168" width="70" height="20" rx="10" fill="#7c3aed" />
        <text x="197" y="178" class="label-tag" fill="#ffffff">AB = ⟨3, 4⟩</text>
      </g>
    </svg>
  </div>

  
  <div class="formula-panel">
    <div class="formula-math" id="formula-main">
      <span class="hl-purple">AB</span> = ⟨4 − 1, 5 − 1⟩ = <span class="hl-purple">⟨3, 4⟩</span> = <span class="hl-blue">v</span>
    </div>
    <div class="formula-desc" id="formula-sub">
      Same run (<span class="hl-orange">+3</span>) and rise (<span class="hl-green">+4</span>) → identical vector
    </div>
  </div>

  <script>
    const stepsData = [
      {
        transformAB: "translate(0px, 0px)",
        opacityAB: "1",
        opacityV: "1",
        showHelpersAB: "1",
        showHelpersV: "1",
        showStandardTag: "0",
        formula: '<span class="hl-purple">AB</span> = ⟨4 − 1, 5 − 1⟩ = <span class="hl-purple">⟨3, 4⟩</span> = <span class="hl-blue">v</span>',
        sub: 'Same horizontal run (<span class="hl-orange">+3</span>) and vertical rise (<span class="hl-green">+4</span>)'
      },
      {
        // 1 unit left (-50px) and 1 unit down (+50px in SVG y) aligns (1,1) directly on (0,0)
        transformAB: "translate(-50px, 50px)",
        opacityAB: "0.85",
        opacityV: "1",
        showHelpersAB: "0",
        showHelpersV: "0",
        showStandardTag: "0",
        formula: '<span class="hl-purple">AB</span> overlays <span class="hl-blue">v</span> directly',
        sub: 'Vectors are invariant under translation (position does not matter)'
      },
      {
        transformAB: "translate(0px, 0px)",
        opacityAB: "0.15",
        opacityV: "1",
        showHelpersAB: "0",
        showHelpersV: "1",
        showStandardTag: "1",
        formula: 'Standard Position: Tail at (0,0) ⟹ Head is (3,4)',
        sub: 'Component form <span class="hl-blue">⟨3, 4⟩</span> matches terminal coordinates exactly'
      }
    ];

    function setStep(index) {
      // Update buttons
      for (let i = 0; i < 3; i++) {
        const btn = document.getElementById('btn-' + i);
        if (i === index) {
          btn.classList.add('active');
        } else {
          btn.classList.remove('active');
        }
      }

      const d = stepsData[index];

      // Apply transformations & opacities
      const groupAB = document.getElementById('group-ab');
      const groupV = document.getElementById('group-v');
      const helpersAB = document.getElementById('helpers-ab');
      const helpersV = document.getElementById('helpers-v');
      const standardTag = document.getElementById('standard-tag');

      groupAB.style.transform = d.transformAB;
      groupAB.style.opacity = d.opacityAB;
      groupV.style.opacity = d.opacityV;

      helpersAB.style.opacity = d.showHelpersAB;
      helpersV.style.opacity = d.showHelpersV;
      standardTag.style.opacity = d.showStandardTag;

      // Update text
      document.getElementById('formula-main').innerHTML = d.formula;
      document.getElementById('formula-sub').innerHTML = d.sub;
    }
  </script>
</body>
</html>

Representing Vectors Geometrically and in Component Form

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <meta name="aspect-ratio" content="4:3">
  <title>Two Ways to Write the Same Vector</title>
  <link rel="stylesheet" href="{{VENDOR_CDN}}/katex.min.css">
  <script src="{{VENDOR_CDN}}/katex.min.js"></script>
  <style>
    * { box-sizing: border-box; margin: 0; padding: 0; }
    body {
      font-family: system-ui, -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
      background: #f8fafc;
      color: #1e293b;
      padding: 10px 12px;
      display: flex;
      flex-direction: column;
      align-items: center;
      gap: 8px;
      min-height: 100%;
    }

    /* Header */
    .header-area {
      text-align: center;
      max-width: 580px;
    }
    .header-title {
      font-size: 16px;
      font-weight: 700;
      color: #0f172a;
      line-height: 1.2;
    }
    .header-sub {
      font-size: 11.5px;
      color: #64748b;
      margin-top: 2px;
    }

    /* Toggle Switch */
    .toggle-bar {
      display: inline-flex;
      background: #e2e8f0;
      padding: 3px;
      border-radius: 9999px;
      gap: 2px;
    }
    .toggle-btn {
      border: none;
      background: transparent;
      padding: 5px 12px;
      font-size: 12px;
      font-weight: 600;
      color: #64748b;
      border-radius: 9999px;
      cursor: pointer;
      transition: background 0.15s ease, color 0.15s ease, box-shadow 0.15s ease;
    }
    .toggle-btn.active {
      background: #ffffff;
      color: #0f172a;
      box-shadow: 0 1px 3px rgba(0,0,0,0.1);
    }

    /* Comparison Area */
    .compare-container {
      width: 100%;
      max-width: 580px;
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 8px;
    }

    .notation-card {
      flex: 1;
      background: #ffffff;
      border: 1px solid #e2e8f0;
      border-radius: 10px;
      padding: 10px 8px;
      display: flex;
      flex-direction: column;
      align-items: center;
      gap: 6px;
      box-shadow: 0 1px 3px rgba(0,0,0,0.04);
      min-width: 0;
    }

    .card-title {
      font-size: 10.5px;
      font-weight: 700;
      text-transform: uppercase;
      letter-spacing: 0.5px;
      color: #64748b;
      text-align: center;
    }

    .math-display {
      font-size: 22px;
      min-height: 56px;
      display: flex;
      align-items: center;
      justify-content: center;
    }

    /* Fallback matrix styling if KaTeX fails */
    .matrix-fallback {
      display: inline-flex;
      align-items: center;
      font-weight: 700;
      font-size: 20px;
    }
    .matrix-paren {
      font-size: 32px;
      font-weight: 300;
      line-height: 1;
      color: #334155;
    }
    .matrix-col {
      display: flex;
      flex-direction: column;
      align-items: center;
      padding: 0 4px;
      gap: 2px;
      font-size: 18px;
    }

    /* Equal Badge Divider */
    .equals-divider {
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      gap: 4px;
      flex-shrink: 0;
    }
    .eq-circle {
      width: 32px;
      height: 32px;
      background: #ecfdf5;
      color: #059669;
      border: 2px solid #a7f3d0;
      border-radius: 50%;
      display: flex;
      align-items: center;
      justify-content: center;
      font-size: 18px;
      font-weight: 800;
    }
    .eq-label {
      font-size: 9.5px;
      font-weight: 700;
      color: #059669;
      background: #ecfdf5;
      padding: 2px 6px;
      border-radius: 6px;
      white-space: nowrap;
    }

    /* Badges */
    .badge-list {
      display: flex;
      flex-direction: column;
      gap: 4px;
      width: 100%;
    }
    .pill-badge {
      display: flex;
      align-items: center;
      font-size: 10.5px;
      font-weight: 600;
      padding: 4px 6px;
      border-radius: 5px;
      background: #f8fafc;
      width: 100%;
      line-height: 1.2;
    }
    .pill-badge.x-badge {
      border-left: 3px solid #2563eb;
      color: #1d4ed8;
      background: #eff6ff;
    }
    .pill-badge.y-badge {
      border-left: 3px solid #e11d48;
      color: #be123c;
      background: #fff1f2;
    }

    /* Visualizer Section */
    .visualizer-strip {
      width: 100%;
      max-width: 580px;
      background: #ffffff;
      border: 1px solid #e2e8f0;
      border-radius: 10px;
      padding: 8px 12px;
      display: flex;
      align-items: center;
      justify-content: space-between;
      gap: 12px;
      box-shadow: 0 1px 3px rgba(0,0,0,0.04);
    }
    .svg-container {
      width: 130px;
      height: 80px;
      flex-shrink: 0;
    }
    svg {
      width: 100%;
      height: 100%;
      overflow: visible;
    }
    .vis-legend {
      flex: 1;
      display: flex;
      flex-direction: column;
      gap: 4px;
      font-size: 11.5px;
      font-weight: 600;
    }
    .legend-item {
      display: flex;
      align-items: center;
      gap: 6px;
    }
    .legend-color {
      width: 9px;
      height: 9px;
      border-radius: 2.5px;
      flex-shrink: 0;
    }

    @media (max-width: 440px) {
      .compare-container {
        gap: 4px;
      }
      .card-title {
        font-size: 9.5px;
      }
      .pill-badge {
        font-size: 9.5px;
        padding: 3px 5px;
      }
      .eq-circle {
        width: 26px;
        height: 26px;
        font-size: 15px;
      }
      .eq-label {
        font-size: 8.5px;
      }
      .svg-container {
        width: 105px;
        height: 70px;
      }
      .vis-legend {
        font-size: 10.5px;
      }
    }
  </style>
</head>
<body>

  
  <div class="header-area">
    <div class="header-title">Two Ways to Write the Same Vector</div>
    <div class="header-sub">Both notations describe identical 2D displacement</div>
  </div>

  
  <div class="toggle-bar" role="tablist">
    <button class="toggle-btn active" id="btn-alg" onclick="setMode('alg')">Algebraic Form</button>
    <button class="toggle-btn" id="btn-num" onclick="setMode('num')">Numeric ⟨4, 3⟩</button>
  </div>

  
  <div class="compare-container">
    
    <div class="notation-card">
      <div class="card-title">Component Form</div>
      <div class="math-display" id="comp-math"></div>
      <div class="badge-list">
        <div class="pill-badge x-badge" id="comp-x-label">x = Horizontal change</div>
        <div class="pill-badge y-badge" id="comp-y-label">y = Vertical change</div>
      </div>
    </div>

    
    <div class="equals-divider">
      <div class="eq-circle">=</div>
      <div class="eq-label">Identical Vector</div>
    </div>

    
    <div class="notation-card">
      <div class="card-title">Column Matrix Form</div>
      <div class="math-display" id="col-math"></div>
      <div class="badge-list">
        <div class="pill-badge x-badge" id="col-x-label">Top row = Horizontal change</div>
        <div class="pill-badge y-badge" id="col-y-label">Bottom row = Vertical change</div>
      </div>
    </div>
  </div>

  
  <div class="visualizer-strip">
    <div class="svg-container">
      <svg viewBox="0 0 130 85">
        <defs>
          <marker id="arr-x" markerWidth="6" markerHeight="6" refX="5" refY="3" orient="auto">
            <path d="M0,0 L6,3 L0,6 Z" fill="#2563eb" />
          </marker>
          <marker id="arr-y" markerWidth="6" markerHeight="6" refX="5" refY="3" orient="auto">
            <path d="M0,0 L6,3 L0,6 Z" fill="#e11d48" />
          </marker>
          <marker id="arr-v" markerWidth="6" markerHeight="6" refX="5" refY="3" orient="auto">
            <path d="M0,0 L6,3 L0,6 Z" fill="#059669" />
          </marker>
        </defs>
        
        <g fill="#cbd5e1">
          <circle cx="15" cy="72" r="1.5"/>
          <circle cx="42" cy="72" r="1.5"/>
          <circle cx="69" cy="72" r="1.5"/>
          <circle cx="96" cy="72" r="1.5"/>
          <circle cx="123" cy="72" r="1.5"/>

          <circle cx="15" cy="51" r="1.5"/>
          <circle cx="42" cy="51" r="1.5"/>
          <circle cx="69" cy="51" r="1.5"/>
          <circle cx="96" cy="51" r="1.5"/>
          <circle cx="123" cy="51" r="1.5"/>

          <circle cx="15" cy="30" r="1.5"/>
          <circle cx="42" cy="30" r="1.5"/>
          <circle cx="69" cy="30" r="1.5"/>
          <circle cx="96" cy="30" r="1.5"/>
          <circle cx="123" cy="30" r="1.5"/>

          <circle cx="15" cy="12" r="1.5"/>
          <circle cx="42" cy="12" r="1.5"/>
          <circle cx="69" cy="12" r="1.5"/>
          <circle cx="96" cy="12" r="1.5"/>
          <circle cx="123" cy="12" r="1.5"/>
        </g>
        
        <line x1="15" y1="72" x2="116" y2="72" stroke="#2563eb" stroke-width="2.2" stroke-dasharray="3,3" marker-end="url(#arr-x)"/>
        
        <line x1="123" y1="72" x2="123" y2="19" stroke="#e11d48" stroke-width="2.2" stroke-dasharray="3,3" marker-end="url(#arr-y)"/>
        
        <line x1="15" y1="72" x2="118" y2="16" stroke="#059669" stroke-width="2.8" marker-end="url(#arr-v)"/>
      </svg>
    </div>
    <div class="vis-legend">
      <div class="legend-item" style="color: #2563eb;">
        <span class="legend-color" style="background: #2563eb;"></span>
        <span id="leg-x">Horizontal: +4 (right)</span>
      </div>
      <div class="legend-item" style="color: #e11d48;">
        <span class="legend-color" style="background: #e11d48;"></span>
        <span id="leg-y">Vertical: +3 (up)</span>
      </div>
      <div class="legend-item" style="color: #059669;">
        <span class="legend-color" style="background: #059669;"></span>
        <span id="leg-res">Resultant: ⟨4, 3⟩</span>
      </div>
    </div>
  </div>

  <script>
    let currentMode = 'alg';

    function renderMath() {
      const isNum = currentMode === 'num';
      const xVal = isNum ? '4' : 'x';
      const yVal = isNum ? '3' : 'y';

      // KaTeX string generation
      const compStr = `\\langle {\\color{#2563eb}{${xVal}}},\\, {\\color{#e11d48}{${yVal}}} \\rangle`;
      const colStr = `\\begin{pmatrix} {\\color{#2563eb}{${xVal}}} \\\\[2pt] {\\color{#e11d48}{${yVal}}} \\end{pmatrix}`;

      if (window.katex) {
        katex.render(compStr, document.getElementById('comp-math'), { throwOnError: false, displayMode: true });
        katex.render(colStr, document.getElementById('col-math'), { throwOnError: false, displayMode: true });
      } else {
        document.getElementById('comp-math').innerHTML = `&langle;<span style="color:#2563eb;font-weight:700;">${xVal}</span>, <span style="color:#e11d48;font-weight:700;">${yVal}</span>&rangle;`;
        document.getElementById('col-math').innerHTML = `
          <div class="matrix-fallback">
            <span class="matrix-paren">(</span>
            <div class="matrix-col">
              <span style="color:#2563eb">${xVal}</span>
              <span style="color:#e11d48">${yVal}</span>
            </div>
            <span class="matrix-paren">)</span>
          </div>
        `;
      }

      // Update badge annotations
      document.getElementById('comp-x-label').textContent = isNum ? 'x = 4 (Horizontal change)' : 'x = Horizontal change';
      document.getElementById('comp-y-label').textContent = isNum ? 'y = 3 (Vertical change)' : 'y = Vertical change';
      document.getElementById('col-x-label').textContent = isNum ? 'Top row = 4 (Horizontal)' : 'Top row = Horizontal change (x)';
      document.getElementById('col-y-label').textContent = isNum ? 'Bottom row = 3 (Vertical)' : 'Bottom row = Vertical change (y)';

      // Update geometric visualizer legend
      document.getElementById('leg-x').textContent = isNum ? 'Horizontal: +4 (right)' : 'Horizontal: x (right / left)';
      document.getElementById('leg-y').textContent = isNum ? 'Vertical: +3 (up)' : 'Vertical: y (up / down)';
      document.getElementById('leg-res').textContent = isNum ? 'Resultant: ⟨4, 3⟩' : 'Resultant: ⟨x, y⟩';
    }

    function setMode(mode) {
      currentMode = mode;
      document.getElementById('btn-alg').classList.toggle('active', mode === 'alg');
      document.getElementById('btn-num').classList.toggle('active', mode === 'num');
      renderMath();
    }

    // Initialize
    window.addEventListener('DOMContentLoaded', () => {
      setMode('alg');
    });
  </script>
</body>
</html>

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <style>
    * {
      box-sizing: border-box;
      margin: 0;
      padding: 0;
    }
    body {
      width: 100%;
      min-height: 100vh;
      background: #f8f9fa;
      font-family: system-ui, -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
      color: #1e2945;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      padding: 12px;
      user-select: none;
    }
    .diagram-wrap {
      width: 100%;
      max-width: 380px;
      display: flex;
      flex-direction: column;
      align-items: center;
      gap: 12px;
    }
    .svg-container {
      width: 100%;
      aspect-ratio: 1 / 1;
      display: flex;
      align-items: center;
      justify-content: center;
    }
    svg {
      width: 100%;
      height: 100%;
      overflow: visible;
    }
    .grid-line {
      stroke: #e2e8f0;
      stroke-width: 1;
    }
    .axis-line {
      stroke: #64748b;
      stroke-width: 1.5;
    }
    .axis-text {
      font-size: 11px;
      fill: #64748b;
      font-weight: 500;
      text-anchor: middle;
      dominant-baseline: middle;
    }
    .point-label {
      font-size: 12px;
      font-weight: 700;
      fill: #1e2945;
    }
    .comp-label {
      font-size: 12px;
      font-weight: 700;
      fill: #0284c7;
      text-anchor: middle;
      dominant-baseline: central;
    }
    .vec-label {
      font-size: 13px;
      font-weight: 700;
      fill: #0284c7;
      text-anchor: middle;
      dominant-baseline: central;
    }
    .dash-path {
      stroke-dasharray: 6 5;
      stroke-dashoffset: 0;
      animation: dashMove 1.5s linear infinite;
    }
    @keyframes dashMove {
      to {
        stroke-dashoffset: -22;
      }
    }
    .controls {
      display: flex;
      gap: 6px;
      width: 100%;
      justify-content: center;
    }
    .btn-step {
      flex: 1;
      padding: 7px 8px;
      font-size: 12px;
      font-weight: 600;
      border-radius: 6px;
      border: 1px solid #cbd5e1;
      background: #ffffff;
      color: #475569;
      cursor: pointer;
      text-align: center;
      transition: background-color 0.2s ease, color 0.2s ease, border-color 0.2s ease;
      box-shadow: 0 1px 2px rgba(0,0,0,0.04);
      display: inline-flex;
      align-items: center;
      justify-content: center;
      gap: 3px;
    }
    .btn-step:hover {
      background: #f1f5f9;
    }
    .btn-step.active {
      background: #0284c7;
      color: #ffffff;
      border-color: #0284c7;
      box-shadow: 0 2px 4px rgba(2, 132, 199, 0.25);
    }
    .vec-symbol {
      display: inline-flex;
      flex-direction: column;
      align-items: center;
      line-height: 1;
      vertical-align: middle;
    }
    .vec-arrow {
      font-size: 9px;
      line-height: 8px;
    }
  </style>
</head>
<body>

  <div class="diagram-wrap">
    <div class="svg-container">
      <svg viewBox="0 0 340 340">
        <defs>
          
          <marker id="arrow" viewBox="0 0 10 10" refX="7" refY="5" markerWidth="6.5" markerHeight="6.5" orient="auto-start-reverse">
            <path d="M 1 1.5 L 8 5 L 1 8.5 z" fill="#0284c7" />
          </marker>
          
          <marker id="comp-arrow-x" viewBox="0 0 10 10" refX="6" refY="5" markerWidth="5" markerHeight="5" orient="auto">
            <path d="M 1 2 L 7 5 L 1 8 z" fill="#0ea5e9" />
          </marker>
          
          <marker id="comp-arrow-y" viewBox="0 0 10 10" refX="6" refY="5" markerWidth="5" markerHeight="5" orient="auto">
            <path d="M 1 2 L 7 5 L 1 8 z" fill="#0ea5e9" />
          </marker>
          
          <filter id="shadow" x="-10%" y="-10%" width="120%" height="130%">
            <feDropShadow dx="0" dy="1.5" stdDeviation="2" flood-color="#000" flood-opacity="0.08" />
          </filter>
        </defs>

        
        
        <g id="grid">
          
          <line x1="73" y1="39" x2="73" y2="305" class="grid-line" />
          <line x1="111" y1="39" x2="111" y2="305" class="grid-line" />
          <line x1="149" y1="39" x2="149" y2="305" class="grid-line" />
          <line x1="187" y1="39" x2="187" y2="305" class="grid-line" />
          <line x1="225" y1="39" x2="225" y2="305" class="grid-line" />
          <line x1="263" y1="39" x2="263" y2="305" class="grid-line" />
          <line x1="301" y1="39" x2="301" y2="305" class="grid-line" />

          
          <line x1="35" y1="267" x2="301" y2="267" class="grid-line" />
          <line x1="35" y1="229" x2="301" y2="229" class="grid-line" />
          <line x1="35" y1="191" x2="301" y2="191" class="grid-line" />
          <line x1="35" y1="153" x2="301" y2="153" class="grid-line" />
          <line x1="35" y1="115" x2="301" y2="115" class="grid-line" />
          <line x1="35" y1="77" x2="301" y2="77" class="grid-line" />
          <line x1="35" y1="39" x2="301" y2="39" class="grid-line" />

          
          <line x1="35" y1="305" x2="315" y2="305" class="axis-line" />
          <line x1="35" y1="305" x2="35" y2="25" class="axis-line" />

          
          
          <text x="35" y="320" class="axis-text">0</text>
          <text x="73" y="320" class="axis-text">1</text>
          <text x="111" y="320" class="axis-text">2</text>
          <text x="149" y="320" class="axis-text">3</text>
          <text x="187" y="320" class="axis-text">4</text>
          <text x="225" y="320" class="axis-text">5</text>
          <text x="263" y="320" class="axis-text">6</text>
          <text x="301" y="320" class="axis-text">7</text>
          <text x="325" y="305" class="axis-text" style="font-weight:700; fill:#1e2945;">x</text>

          
          <text x="20" y="267" class="axis-text">1</text>
          <text x="20" y="229" class="axis-text">2</text>
          <text x="20" y="191" class="axis-text">3</text>
          <text x="20" y="153" class="axis-text">4</text>
          <text x="20" y="115" class="axis-text">5</text>
          <text x="20" y="77" class="axis-text">6</text>
          <text x="20" y="39" class="axis-text">7</text>
          <text x="35" y="14" class="axis-text" style="font-weight:700; fill:#1e2945;">y</text>
        </g>

        
        <g id="components-layer" opacity="1" style="transition: opacity 0.3s ease;">
          
          <line x1="73" y1="229" x2="220" y2="229" stroke="#0ea5e9" stroke-width="2.5" class="dash-path" marker-end="url(#comp-arrow-x)" />
          <rect x="135" y="238" width="30" height="18" rx="4" fill="#ffffff" stroke="#bae6fd" />
          <text x="150" y="247" class="comp-label">+4</text>

          
          <line x1="225" y1="229" x2="225" y2="122" stroke="#0ea5e9" stroke-width="2.5" class="dash-path" marker-end="url(#comp-arrow-y)" />
          <rect x="233" y="163" width="30" height="18" rx="4" fill="#ffffff" stroke="#bae6fd" />
          <text x="248" y="172" class="comp-label">+3</text>
        </g>

        
        <g id="vector-layer" opacity="1" style="transition: opacity 0.3s ease;">
          <line x1="73" y1="229" x2="220" y2="119" stroke="#0284c7" stroke-width="4" stroke-linecap="round" marker-end="url(#arrow)" />
          
          
          <g transform="translate(100, 150)">
            <rect x="0" y="0" width="88" height="24" rx="5" fill="#ffffff" stroke="#bae6fd" stroke-width="1.5" filter="url(#shadow)" />
            
            <text x="17" y="13" class="vec-label" font-style="italic">v</text>
            
            <path d="M 12 5.5 L 21 5.5 M 19 3.5 L 21.5 5.5 L 19 7.5" fill="none" stroke="#0284c7" stroke-width="1.1" stroke-linecap="round" stroke-linejoin="round" />
            <text x="54" y="13" class="vec-label" font-weight="700"> = &lang;4, 3&rang;</text>
          </g>
        </g>

        
        <g id="points-layer">
          
          <circle cx="73" cy="229" r="5.5" fill="#0284c7" stroke="#ffffff" stroke-width="2" />
          <text x="66" y="250" class="point-label" text-anchor="end">A (1, 2)</text>

          
          <circle cx="225" cy="115" r="3.5" fill="#0284c7" opacity="0.8" />
          <text x="234" y="106" class="point-label" text-anchor="start">B (5, 5)</text>
        </g>
      </svg>
    </div>

    
    <div class="controls">
      <button class="btn-step active" id="btn-all" onclick="setMode('all')">Full Vector</button>
      <button class="btn-step" id="btn-comp" onclick="setMode('comp')">Components (+4, +3)</button>
      <button class="btn-step" id="btn-vec" onclick="setMode('vec')">
        Vector 
        <span class="vec-symbol">
          <span class="vec-arrow">&rarr;</span>
          <i>v</i>
        </span>
      </button>
    </div>
  </div>

  <script>
    function setMode(mode) {
      const compLayer = document.getElementById('components-layer');
      const vecLayer = document.getElementById('vector-layer');
      
      document.querySelectorAll('.btn-step').forEach(btn => btn.classList.remove('active'));

      if (mode === 'all') {
        compLayer.style.opacity = '1';
        vecLayer.style.opacity = '1';
        document.getElementById('btn-all').classList.add('active');
      } else if (mode === 'comp') {
        compLayer.style.opacity = '1';
        vecLayer.style.opacity = '0.15';
        document.getElementById('btn-comp').classList.add('active');
      } else if (mode === 'vec') {
        compLayer.style.opacity = '0.15';
        vecLayer.style.opacity = '1';
        document.getElementById('btn-vec').classList.add('active');
      }
    }
  </script>
</body>
</html>

OGM.11.GEO.7

Aligned learning resources

Related diagrams