lesson
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Imagine dropping into a massive video game world with just two straight roads crossing right in the middle. How could you give your friend exact directions to your secret base anywhere on the map?
The Two Main Roads
We pinpoint any location using a coordinate plane, which is built from two number lines crossing at right angles.
The flat horizontal line is the x-axis, while the tall vertical line is the y-axis.
Where the two axes cross at zero is the origin, written as the coordinate pair (0,0). In 1637, French thinker René Descartes invented this system to connect geometry with numbers after watching a fly crawl across his ceiling.
📊A clean, modern coordinate grid diagram. Draw horizontal x-axis and vertical y-axis crossing at center (0,0). Label the horizontal line 'x-axis' with positive numbers to the right and negative to the left. Label the vertical line 'y-axis' with positive numbers going up and negative going down. Highlight the center intersection with a glowing blue dot and label it 'Origin (0,0)'. Crisp minimalist style, dark blue text #1e2945, soft gray gridlines, bright cyan/blue highlight on the origin, viewBox 0 0 400 400, responsive design.
When these two infinite lines cross, they slice the flat plane into distinct zones — but how many regions do they make, and how do we name them?
The Four Quadrants
The two axes divide the grid into four separate regions called quadrants (from the Latin word for 'four').
We number them using Roman numerals (I, II, III, IV), starting in the top-right and moving counterclockwise like making a giant letter 'C'.
📊A square coordinate plane visual showing the 4 quadrants labeled with large bold Roman numerals: Quadrant I (top-right, soft green background tint), Quadrant II (top-left, soft orange background tint), Quadrant III (bottom-left, soft purple background tint), Quadrant IV (bottom-right, soft red background tint). Draw a curved directional arrow starting in Quadrant I, curving left through II, down into III, and ending in IV to show the counterclockwise numbering order. Crisp labels and clear axis lines.
Since each quadrant sits on different sides of zero, can we tell where a point lands just by looking at its positive and negative signs?