The Coordinate Plane

Geometry · Axiom Academy

Where algebra meets geometry — every location is just a pair of numbers. Pinning down any spot with two numbers The coordinate plane (also called the Cartesian plane, after René Descartes) is a flat surface where we can plot points, draw shapes, and connect algebra with geometry. Every location on it is described by an ordered pair (x, y) — and that simple idea is what lets us attack geometry with equations. Watch how a single point gets placed. To plot (3, 2) , start at the origin, walk right 3 along the x -axis, then up 2 parallel to the y -axis. Then watch what happens if you swap the numbers and plot (2, 3) instead — it lands somewhere different . The order is everything. An ordered pair (x, y) is a recipe: how far across, then how far up. Swap them and you get a different point — that's why it's an ordered pair. Drag the point — or use the sliders — and watch its ordered pair (x, y) update. The dashed legs show the horizontal and vertical distances from the origin, and the readout names the quadrant it lands in. x first (across), y second (up) — the order is what makes it an ordered pair. The axes divide the plane into four regions called quadrants , numbered counterclockwise starting from the upper right. Watch each one light up in turn — a sample point lands in it and its sign pattern appears. Each one is defined by the signs of its coordinates. Counterclockwise from the top-right: I (+,+) → II (-,+) → III (-,-) → IV (+,-) . Upper right: x positive, y positive

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