<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <title>Distance Formula Breakdown</title>
  <style>
    * {
      box-sizing: border-box;
      margin: 0;
      padding: 0;
    }

    body {
      font-family: system-ui, -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
      background-color: #f8fafc;
      color: #1e293b;
      padding: 16px 12px;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      min-height: 100vh;
    }

    .breakdown-container {
      width: 100%;
      max-width: 350px;
      display: flex;
      flex-direction: column;
      gap: 12px;
    }

    /* Formula Header */
    .formula-box {
      background: #ffffff;
      border: 1px solid #e2e8f0;
      border-radius: 12px;
      padding: 14px 12px;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      box-shadow: 0 1px 3px rgba(0, 0, 0, 0.05);
    }

    .formula-row {
      display: inline-flex;
      align-items: center;
      justify-content: center;
      font-size: 20px;
      font-weight: 700;
      letter-spacing: -0.2px;
      user-select: none;
    }

    .math-d {
      color: #0f172a;
      font-style: italic;
      font-family: "Times New Roman", Times, serif;
      margin-right: 6px;
      font-size: 22px;
    }

    .math-eq {
      color: #64748b;
      margin-right: 6px;
    }

    .math-radical {
      font-size: 28px;
      font-weight: 300;
      color: #7c3aed;
      cursor: pointer;
      line-height: 1;
      padding: 2px 2px 2px 4px;
      border-radius: 4px;
      transition: opacity 0.2s, background-color 0.2s;
    }

    .math-radical:focus-visible,
    .math-term:focus-visible,
    .pill-item:focus-visible {
      outline: 2px solid #7c3aed;
      outline-offset: 2px;
    }

    .math-vinculum {
      display: inline-flex;
      align-items: center;
      border-top: 2.5px solid #7c3aed;
      padding-top: 4px;
      margin-left: -1px;
      gap: 4px;
    }

    .math-term {
      padding: 3px 8px;
      border-radius: 6px;
      font-size: 15px;
      cursor: pointer;
      transition: opacity 0.2s ease, border-color 0.2s ease, background-color 0.2s ease;
      display: inline-flex;
      align-items: center;
      line-height: 1;
    }

    .math-term sub {
      font-size: 10px;
      line-height: 0;
      position: relative;
      bottom: -4px;
      margin-left: 1px;
    }

    .math-term sup {
      font-size: 11px;
      font-weight: 800;
      line-height: 0;
      position: relative;
      top: -6px;
      margin-left: 2px;
    }

    .math-dx {
      background: #e0f2fe;
      color: #0369a1;
      border: 1.5px solid #38bdf8;
    }

    .math-plus {
      color: #64748b;
      font-weight: 600;
      font-size: 16px;
      padding: 0 1px;
    }

    .math-dy {
      background: #ffedd5;
      color: #c2410c;
      border: 1.5px solid #fb923c;
    }

    /* Breakdown callouts */
    .pills-container {
      display: flex;
      flex-direction: column;
      gap: 8px;
    }

    .pill-item {
      display: flex;
      align-items: center;
      gap: 10px;
      padding: 9px 12px;
      border-radius: 10px;
      font-size: 13px;
      font-weight: 600;
      border: 1.5px solid transparent;
      cursor: pointer;
      transition: border-color 0.15s ease, background-color 0.15s ease, box-shadow 0.15s ease;
    }

    .pill-radical {
      background: #f5f3ff;
      border-color: #e9d5ff;
      color: #6d28d9;
    }

    .pill-radical.active {
      border-color: #7c3aed;
      background: #ede9fe;
      box-shadow: 0 2px 6px rgba(124, 58, 237, 0.15);
    }

    .pill-dx {
      background: #f0f9ff;
      border-color: #bae6fd;
      color: #0369a1;
    }

    .pill-dx.active {
      border-color: #0284c7;
      background: #e0f2fe;
      box-shadow: 0 2px 6px rgba(2, 132, 199, 0.15);
    }

    .pill-dy {
      background: #fff7ed;
      border-color: #fed7aa;
      color: #c2410c;
    }

    .pill-dy.active {
      border-color: #ea580c;
      background: #ffedd5;
      box-shadow: 0 2px 6px rgba(194, 65, 12, 0.15);
    }

    .pill-symbol {
      width: 24px;
      height: 24px;
      display: flex;
      align-items: center;
      justify-content: center;
      border-radius: 6px;
      font-size: 14px;
      font-weight: 800;
      flex-shrink: 0;
    }

    .pill-radical .pill-symbol {
      background: #ede9fe;
      color: #7c3aed;
    }

    .pill-radical.active .pill-symbol {
      background: #7c3aed;
      color: #ffffff;
    }

    .pill-dx .pill-symbol {
      background: #e0f2fe;
      color: #0284c7;
    }

    .pill-dx.active .pill-symbol {
      background: #0284c7;
      color: #ffffff;
    }

    .pill-dy .pill-symbol {
      background: #ffedd5;
      color: #c2410c;
    }

    .pill-dy.active .pill-symbol {
      background: #ea580c;
      color: #ffffff;
    }

    .pill-text {
      line-height: 1.3;
    }

    /* Mini visual coordinate preview */
    .mini-grid {
      background: #ffffff;
      border: 1px solid #e2e8f0;
      border-radius: 12px;
      padding: 10px 8px;
      display: flex;
      justify-content: center;
      align-items: center;
      box-shadow: 0 1px 3px rgba(0, 0, 0, 0.05);
    }

    svg {
      width: 100%;
      max-width: 260px;
      height: 115px;
      display: block;
    }

    .svg-interactive {
      cursor: pointer;
      transition: opacity 0.2s, stroke-width 0.2s;
    }

    @media (min-width: 600px) {
      .breakdown-container {
        max-width: 420px;
        gap: 14px;
      }
      .formula-row {
        font-size: 22px;
      }
      .math-term {
        font-size: 16px;
        padding: 4px 10px;
      }
      .pill-item {
        padding: 10px 14px;
        font-size: 14px;
      }
    }
  </style>
</head>
<body>

  <div class="breakdown-container">
    
    <div class="formula-box">
      <div class="formula-row" role="region" aria-label="Distance Formula">
        <span class="math-d">d</span>
        <span class="math-eq">=</span>
        <span class="math-radical" id="mathRadical" onclick="selectPart('rad')" role="button" tabindex="0" title="Undo the square to get straight-line distance">√</span>
        <span class="math-vinculum">
          <span class="math-term math-dx" id="mathDx" onclick="selectPart('dx')" role="button" tabindex="0" title="Horizontal change squared">
            (x<sub>2</sub> − x<sub>1</sub>)<sup>2</sup>
          </span>
          <span class="math-plus">+</span>
          <span class="math-term math-dy" id="mathDy" onclick="selectPart('dy')" role="button" tabindex="0" title="Vertical change squared">
            (y<sub>2</sub> − y<sub>1</sub>)<sup>2</sup>
          </span>
        </span>
      </div>
    </div>

    
    <div class="pills-container">
      <div class="pill-item pill-dx active" id="pillDx" onclick="selectPart('dx')" role="button" tabindex="0">
        <div class="pill-symbol">↔</div>
        <div class="pill-text">Horizontal change squared: (x₂ − x₁)²</div>
      </div>

      <div class="pill-item pill-dy" id="pillDy" onclick="selectPart('dy')" role="button" tabindex="0">
        <div class="pill-symbol">↕</div>
        <div class="pill-text">Vertical change squared: (y₂ − y₁)²</div>
      </div>

      <div class="pill-item pill-radical" id="pillRad" onclick="selectPart('rad')" role="button" tabindex="0">
        <div class="pill-symbol">√</div>
        <div class="pill-text">Undo the square to get straight-line distance</div>
      </div>
    </div>

    
    <div class="mini-grid">
      <svg viewBox="0 0 220 100" xmlns="http://www.w3.org/2000/svg">
        
        <line x1="20" y1="20" x2="200" y2="20" stroke="#f1f5f9" stroke-width="1.5" />
        <line x1="20" y1="50" x2="200" y2="50" stroke="#f1f5f9" stroke-width="1.5" />
        <line x1="20" y1="80" x2="200" y2="80" stroke="#f1f5f9" stroke-width="1.5" />
        <line x1="50" y1="10" x2="50" y2="90" stroke="#f1f5f9" stroke-width="1.5" />
        <line x1="105" y1="10" x2="105" y2="90" stroke="#f1f5f9" stroke-width="1.5" />
        <line x1="165" y1="10" x2="165" y2="90" stroke="#f1f5f9" stroke-width="1.5" />

        
        <path d="M 153 75 L 153 63 L 165 63" fill="none" stroke="#cbd5e1" stroke-width="1.5" />

        
        
        <line id="svgDx" class="svg-interactive" onclick="selectPart('dx')" x1="45" y1="75" x2="165" y2="75" stroke="#0284c7" stroke-width="3.5" stroke-linecap="round" />
        
        <line id="svgDy" class="svg-interactive" onclick="selectPart('dy')" x1="165" y1="75" x2="165" y2="25" stroke="#c2410c" stroke-width="3.5" stroke-linecap="round" />
        
        <line id="svgD" class="svg-interactive" onclick="selectPart('rad')" x1="45" y1="75" x2="165" y2="25" stroke="#7c3aed" stroke-width="3.5" stroke-linecap="round" />

        
        <circle cx="45" cy="75" r="4.5" fill="#0f172a" />
        <text x="32" y="90" fill="#64748b" font-size="9" font-weight="600" text-anchor="middle">(x₁, y₁)</text>

        <circle cx="165" cy="25" r="4.5" fill="#0f172a" />
        <text x="178" y="18" fill="#64748b" font-size="9" font-weight="600" text-anchor="middle">(x₂, y₂)</text>

        
        <text id="lblDx" class="svg-interactive" onclick="selectPart('dx')" x="105" y="92" fill="#0369a1" font-size="11" font-weight="700" text-anchor="middle">x₂ − x₁</text>
        <text id="lblDy" class="svg-interactive" onclick="selectPart('dy')" x="195" y="54" fill="#c2410c" font-size="11" font-weight="700" text-anchor="middle">y₂ − y₁</text>
        <text id="lblD" class="svg-interactive" onclick="selectPart('rad')" x="96" y="44" fill="#7c3aed" font-size="13" font-weight="800" text-anchor="middle">d</text>
      </svg>
    </div>
  </div>

  <script>
    function selectPart(part) {
      const pillDx = document.getElementById('pillDx');
      const pillDy = document.getElementById('pillDy');
      const pillRad = document.getElementById('pillRad');

      const mathDx = document.getElementById('mathDx');
      const mathDy = document.getElementById('mathDy');
      const mathRad = document.getElementById('mathRadical');

      const svgDx = document.getElementById('svgDx');
      const svgDy = document.getElementById('svgDy');
      const svgD = document.getElementById('svgD');

      const lblDx = document.getElementById('lblDx');
      const lblDy = document.getElementById('lblDy');
      const lblD = document.getElementById('lblD');

      // Reset
      [pillDx, pillDy, pillRad].forEach(p => p.classList.remove('active'));
      
      mathDx.style.opacity = '0.35';
      mathDy.style.opacity = '0.35';
      mathRad.style.opacity = '0.35';

      svgDx.setAttribute('stroke-width', '2');
      svgDy.setAttribute('stroke-width', '2');
      svgD.setAttribute('stroke-width', '2');
      
      svgDx.style.opacity = '0.3';
      svgDy.style.opacity = '0.3';
      svgD.style.opacity = '0.3';

      lblDx.style.opacity = '0.3';
      lblDy.style.opacity = '0.3';
      lblD.style.opacity = '0.3';

      if (part === 'dx') {
        pillDx.classList.add('active');
        mathDx.style.opacity = '1';
        svgDx.setAttribute('stroke-width', '4.5');
        svgDx.style.opacity = '1';
        lblDx.style.opacity = '1';
      } else if (part === 'dy') {
        pillDy.classList.add('active');
        mathDy.style.opacity = '1';
        svgDy.setAttribute('stroke-width', '4.5');
        svgDy.style.opacity = '1';
        lblDy.style.opacity = '1';
      } else if (part === 'rad') {
        pillRad.classList.add('active');
        mathRad.style.opacity = '1';
        mathDx.style.opacity = '1';
        mathDy.style.opacity = '1';
        svgD.setAttribute('stroke-width', '4.5');
        svgD.style.opacity = '1';
        lblD.style.opacity = '1';
      }
    }

    // Support keyboard activation for accessibility
    document.querySelectorAll('[role="button"]').forEach(el => {
      el.addEventListener('keydown', (e) => {
        if (e.key === 'Enter' || e.key === ' ') {
          e.preventDefault();
          el.click();
        }
      });
    });

    // Default view: highlight horizontal change
    selectPart('dx');
  </script>
</body>
</html>

Finding Distance Between Two Points in the 2D Coordinate Plane

<!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">
  <style>
    * { box-sizing: border-box; margin: 0; padding: 0; }
    body {
      font-family: system-ui, -apple-system, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif;
      color: #0f172a;
      background: transparent;
      display: flex;
      flex-direction: column;
      padding: 10px;
      gap: 8px;
      user-select: none;
      -webkit-user-select: none;
      max-width: 680px;
      margin: 0 auto;
    }
    .header-title {
      text-align: center;
      font-size: 14px;
      font-weight: 700;
      color: #334155;
      letter-spacing: -0.01em;
    }
    .layout {
      display: flex;
      flex-direction: row;
      align-items: center;
      justify-content: center;
      gap: 14px;
      width: 100%;
      flex: 1;
    }
    @media (max-width: 500px) {
      .layout {
        flex-direction: column-reverse;
        gap: 8px;
      }
      .graph-panel {
        max-width: 220px !important;
      }
      .step-card {
        padding: 5px 8px !important;
      }
      .step-math {
        font-size: 12px !important;
      }
    }
    .graph-panel {
      flex: 1;
      display: flex;
      justify-content: center;
      align-items: center;
      max-width: 260px;
      width: 100%;
      aspect-ratio: 1;
    }
    svg {
      width: 100%;
      height: 100%;
      overflow: visible;
    }
    .svg-text {
      font-family: system-ui, -apple-system, sans-serif;
      paint-order: stroke fill;
      stroke: #ffffff;
      stroke-width: 2.5px;
      stroke-linejoin: round;
    }
    .steps-panel {
      flex: 1.3;
      display: flex;
      flex-direction: column;
      gap: 6px;
      width: 100%;
      max-width: 340px;
    }
    .step-card {
      padding: 7px 10px;
      border-radius: 8px;
      background: #f8fafc;
      border: 1.5px solid #e2e8f0;
      opacity: 0.4;
      transition: opacity 0.25s ease, border-color 0.25s ease, background-color 0.25s ease, box-shadow 0.25s ease;
      cursor: pointer;
      display: flex;
      align-items: center;
      gap: 9px;
    }
    .step-card:hover {
      opacity: 0.75;
      background: #ffffff;
      border-color: #cbd5e1;
    }
    .step-card.active {
      opacity: 1;
      background: #ffffff;
      border-color: #0284c7;
      box-shadow: 0 2px 8px rgba(2, 132, 199, 0.16);
    }
    .step-num {
      width: 22px;
      height: 22px;
      border-radius: 50%;
      background: #e2e8f0;
      color: #475569;
      display: flex;
      align-items: center;
      justify-content: center;
      font-size: 11px;
      font-weight: 700;
      flex-shrink: 0;
      transition: background-color 0.25s, color 0.25s;
    }
    .step-card.active .step-num {
      background: #0284c7;
      color: #ffffff;
    }
    .step-content {
      display: flex;
      flex-direction: column;
      gap: 1px;
    }
    .step-label {
      font-size: 10.5px;
      font-weight: 600;
      color: #64748b;
      text-transform: uppercase;
      letter-spacing: 0.03em;
    }
    .step-card.active .step-label {
      color: #0369a1;
    }
    .step-math {
      font-size: 13px;
      font-weight: 500;
      line-height: 1.25;
      color: #0f172a;
      font-family: 'Cambria Math', 'Times New Roman', serif, system-ui;
    }
    .step-math strong {
      font-weight: 700;
      color: #0f172a;
    }
    .controls {
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 8px;
      margin-top: 2px;
    }
    .btn {
      background: #f1f5f9;
      border: 1px solid #cbd5e1;
      border-radius: 6px;
      padding: 4px 10px;
      font-size: 12px;
      font-weight: 600;
      color: #334155;
      cursor: pointer;
      display: inline-flex;
      align-items: center;
      justify-content: center;
      min-width: 28px;
      height: 28px;
      transition: background-color 0.2s, border-color 0.2s;
    }
    .btn:hover {
      background: #e2e8f0;
      border-color: #94a3b8;
    }
    .dots {
      display: flex;
      gap: 6px;
      align-items: center;
    }
    .dot {
      width: 8px;
      height: 8px;
      border-radius: 50%;
      background: #cbd5e1;
      cursor: pointer;
      transition: background-color 0.25s;
    }
    .dot.active {
      background: #0284c7;
      width: 10px;
      height: 10px;
    }
    /* SVG Element Highlights */
    .leg-x { stroke: #0284c7; stroke-width: 3; transition: all 0.25s; }
    .leg-y { stroke: #ea580c; stroke-width: 3; transition: all 0.25s; }
    .hyp { stroke: #6d28d9; stroke-width: 3.5; transition: all 0.25s; }
  </style>
</head>
<body>

  <div class="header-title">Distance Formula: Point A(−3, 2) to Point B(5, −4)</div>

  <div class="layout">
    
    <div class="graph-panel">
      <svg viewBox="-70 -70 140 140" id="coordSvg">
        <defs>
          <marker id="arrow" viewBox="0 0 6 6" refX="5" refY="3" markerWidth="4" markerHeight="4" orient="auto">
            <path d="M 0 1.5 L 4.5 3 L 0 4.5 z" fill="#64748b" />
          </marker>
        </defs>

        
        <g stroke="#e2e8f0" stroke-width="0.8">
          <line x1="-60" y1="-60" x2="-60" y2="60" /><line x1="-50" y1="-60" x2="-50" y2="60" />
          <line x1="-40" y1="-60" x2="-40" y2="60" /><line x1="-30" y1="-60" x2="-30" y2="60" />
          <line x1="-20" y1="-60" x2="-20" y2="60" /><line x1="-10" y1="-60" x2="-10" y2="60" />
          <line x1="10" y1="-60" x2="10" y2="60" /><line x1="20" y1="-60" x2="20" y2="60" />
          <line x1="30" y1="-60" x2="30" y2="60" /><line x1="40" y1="-60" x2="40" y2="60" />
          <line x1="50" y1="-60" x2="50" y2="60" /><line x1="60" y1="-60" x2="60" y2="60" />
          <line x1="-60" y1="-60" x2="60" y2="-60" /><line x1="-60" y1="-50" x2="60" y2="-50" />
          <line x1="-60" y1="-40" x2="60" y2="-40" /><line x1="-60" y1="-30" x2="60" y2="-30" />
          <line x1="-60" y1="-20" x2="60" y2="-20" /><line x1="-60" y1="-10" x2="60" y2="-10" />
          <line x1="-60" y1="10" x2="60" y2="10" /><line x1="-60" y1="20" x2="60" y2="20" />
          <line x1="-60" y1="30" x2="60" y2="30" /><line x1="-60" y1="40" x2="60" y2="40" />
          <line x1="-60" y1="50" x2="60" y2="50" /><line x1="-60" y1="60" x2="60" y2="60" />
        </g>

        
        <line x1="-65" y1="0" x2="65" y2="0" stroke="#64748b" stroke-width="1.2" marker-end="url(#arrow)" />
        <line x1="0" y1="65" x2="0" y2="-65" stroke="#64748b" stroke-width="1.2" marker-end="url(#arrow)" />

        
        <text x="64" y="-3" font-size="6" font-weight="bold" fill="#64748b" text-anchor="end" class="svg-text">x</text>
        <text x="4" y="-60" font-size="6" font-weight="bold" fill="#64748b" text-anchor="start" class="svg-text">y</text>

        
        <path d="M 44 -20 L 44 -14 L 50 -14" fill="none" stroke="#475569" stroke-width="1" />

        
        <line id="svgLegX" class="leg-x" x1="-30" y1="-20" x2="50" y2="-20" stroke-dasharray="3 2" />
        <line id="svgLegY" class="leg-y" x1="50" y1="-20" x2="50" y2="40" stroke-dasharray="3 2" />
        <line id="svgHyp" class="hyp" x1="-30" y1="-20" x2="50" y2="40" />

        
        <circle cx="-30" cy="-20" r="3.5" fill="#0284c7" stroke="#ffffff" stroke-width="1" />
        <circle cx="50" cy="40" r="3.5" fill="#ea580c" stroke="#ffffff" stroke-width="1" />
        <circle cx="50" cy="-20" r="2.5" fill="#64748b" stroke="#ffffff" stroke-width="0.8" />

        
        <text x="-32" y="-24" font-size="7.5" font-weight="bold" fill="#0369a1" text-anchor="end" class="svg-text">A(−3, 2)</text>
        <text x="52" y="49" font-size="7.5" font-weight="bold" fill="#c2410c" text-anchor="start" class="svg-text">B(5, −4)</text>

        
        <text id="lblX" x="10" y="-24" font-size="9" font-weight="bold" fill="#0369a1" text-anchor="middle" class="svg-text">8</text>
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        <text id="lblHyp" x="5" y="16" font-size="10" font-weight="bold" fill="#5b21b6" text-anchor="end" class="svg-text">10</text>
      </svg>
    </div>

    
    <div class="steps-panel">
      <div class="step-card active" data-step="0">
        <div class="step-num">1</div>
        <div class="step-content">
          <div class="step-label">Subtract x-coordinates</div>
          <div class="step-math">Δx = 5 − (−3) = <strong>8</strong></div>
        </div>
      </div>
      <div class="step-card" data-step="1">
        <div class="step-num">2</div>
        <div class="step-content">
          <div class="step-label">Subtract y-coordinates</div>
          <div class="step-math">Δy = −4 − 2 = −6 → |−6| = <strong>6</strong></div>
        </div>
      </div>
      <div class="step-card" data-step="2">
        <div class="step-num">3</div>
        <div class="step-content">
          <div class="step-label">Square both legs</div>
          <div class="step-math">8² + (−6)² = 64 + 36 = <strong>100</strong></div>
        </div>
      </div>
      <div class="step-card" data-step="3">
        <div class="step-num">4</div>
        <div class="step-content">
          <div class="step-label">Take square root</div>
          <div class="step-math">d = √(64 + 36) = √100 = <strong>10</strong></div>
        </div>
      </div>
    </div>
  </div>

  
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<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <title>Distance Formula Grid</title>
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    .label-dy {
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      justify-content: center;
      gap: 8px;
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      flex: 1;
      padding: 8px 6px;
      font-size: 12.5px;
      font-weight: 600;
      background: #f1f5f9;
      color: #334155;
      border: 1px solid #cbd5e1;
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      cursor: pointer;
      text-align: center;
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      text-align: center;
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    .highlight-orange {
      color: #c2410c;
      font-weight: 700;
    }
  </style>
</head>
<body>
  <div class="diagram-wrap">
    <div class="grid-container">
      <svg viewBox="0 0 380 240" aria-label="Coordinate grid showing distance formula and right triangle legs between points P1 and P2">
        <defs>
          <marker id="arrow" viewBox="0 0 10 10" refX="5" refY="5" markerWidth="6" markerHeight="6" orient="auto-start-reverse">
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        <line class="grid-line" x1="40" y1="25" x2="40" y2="215" />
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        <text class="axis-label" x="40" y="228">0</text>
        <text class="axis-label" x="80" y="228">1</text>
        <text class="axis-label" x="120" y="228">2</text>
        <text class="axis-label" x="160" y="228">3</text>
        <text class="axis-label" x="200" y="228">4</text>
        <text class="axis-label" x="240" y="228">5</text>
        <text class="axis-label" x="280" y="228">6</text>
        <text class="axis-label" x="320" y="228">7</text>
        <text class="axis-label" x="355" y="215">x</text>

        <text class="axis-label" x="26" y="177">1</text>
        <text class="axis-label" x="26" y="139">2</text>
        <text class="axis-label" x="26" y="101">3</text>
        <text class="axis-label" x="26" y="63">4</text>
        <text class="axis-label" x="26" y="25">5</text>
        <text class="axis-label" x="40" y="8">y</text>

        
        <path id="rightAngle" class="right-angle" d="M 268 177 L 268 165 L 280 165" />

        
        
        <line id="legX" class="leg-line" x1="120" y1="177" x2="280" y2="177" />
        
        <line id="legY" class="leg-line" x1="280" y1="177" x2="280" y2="63" />

        
        <line id="lineD" class="dist-line" x1="120" y1="177" x2="280" y2="63" />

        
        <text id="labelX" class="math-label label-dx" x="200" y="196">Δx = x₂ − x₁ = 4</text>
        <text id="labelY" class="math-label label-dy" x="288" y="124">Δy = y₂ − y₁ = 3</text>

        
        <text id="labelD" class="label-d" x="186" y="106">d (distance)</text>

        
        <circle id="ptCorner" class="pt-corner" cx="280" cy="177" r="3.5" />

        
        <circle class="pt-p1" cx="120" cy="177" r="6" />
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        <circle class="pt-p2" cx="280" cy="63" r="6" />
        <text class="pt-label" x="288" y="55" text-anchor="start">P₂(6, 4)</text>
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      <button class="btn-step" id="step1" onclick="setStep(1)">2. Legs (Δx, Δy)</button>
      <button class="btn-step" id="step2" onclick="setStep(2)">3. Pythagorean</button>
    </div>

    
    <div class="info-bar" id="infoText">
      Distance <span class="highlight-blue">&nbsp;d&nbsp;</span> connecting P₁(2, 1) and P₂(6, 4)
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</body>
</html>

Finding Midpoints and Partitioning Segments in 2D

Specifying Position Using Azimuth and Bearings

Solving Navigation Problems with Bearings and Distance

Representing Polygons and Circles Algebraically in the Coordinate Plane

Introduction to the 3D Cartesian Coordinate System

Plotting Points and Specifying Positions in 3D Space

Calculating Distance Between Points in 3D Space

Representing 3D Solids and Planes Algebraically

math

Coordinate Geometry in 2D and 3D: Distance, Bearings, and Shapes

Describing Position in Three Dimensions

Using 3D Coordinate Systems

Using Digital Tools to Solve Spatial Problems

Designing Algorithms to Test Congruency and Similarity

Spatial Reasoning and Computational Geometry

平面上确定位置的方法与有序数对的概念

平面直角坐标系的概念：x轴、y轴、原点与四个象限

点的坐标确定与由坐标描点（横坐标与纵坐标）

各象限及坐标轴上点的坐标正负符号特征规律

平行于坐标轴的直线上点的坐标特征与距离公式

在实际生活情境中建立适当的平面直角坐标系描述物体位置

给定正方形等几何图形的坐标系选择与顶点坐标表达

运用方位角和距离刻画两个物体的相对位置（极坐标初步）

坐标平面内几何图形面积的计算：割补法与铅垂高模型

平面直角坐标系的建立与位置确定

关于 x 轴和 y 轴对称的点的坐标变化规律

关于原点对称（中心对称）的点的坐标变化规律

以坐标轴为对称轴的多边形对称图形绘制与顶点坐标变换

沿单一坐标轴方向平移时点的坐标变化规律（“左减右加，上加下减”）

多边形沿坐标轴方向平移一定距离后图形的顶点坐标确定

多边形依次沿两个坐标轴方向平移后的复合平移关系与顶点坐标

以原点为位似中心时坐标按倍数放缩与位似图形的生成

图形与坐标单元体系总结与尺规作图前瞻衔接

图形的运动与坐标变换规律

OGM.9.FN.5

OGM.9.FN.5

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