How the coordinate plane works
The coordinate plane (or Cartesian plane) is built from two number lines that cross at the origin — the horizontal x-axis and the vertical y-axis. Every point is named by an ordered pair (x, y): how far right or left along the x-axis, then how far up or down along the y-axis.
Drag the point above (or use the arrow keys when it’s focused) and watch its coordinates update. The dashed guides show exactly how far the point sits from each axis.
The four quadrants
The axes split the plane into four quadrants, numbered counter-clockwise starting from the top right:
- Quadrant I: x positive, y positive — (+, +)
- Quadrant II: x negative, y positive — (−, +)
- Quadrant III: x negative, y negative — (−, −)
- Quadrant IV: x positive, y negative — (+, −)
Points that land on an axis (like (3, 0) or (0, −2)) belong to no quadrant — drag onto an axis to see that called out.
Reflections
Turn on show reflections to see what happens to a point’s coordinates when you flip it:
- Across the x-axis: the sign of y flips → (x, −y)
- Across the y-axis: the sign of x flips → (−x, y)
- Through the origin: both signs flip → (−x, −y)
Spotting that “reflecting changes a sign” is the same pattern that powers symmetry later — including the sign rules on the unit circle.
Using this with a class
Project it and call out a coordinate before plotting, or give a quadrant and ask a student to drag the point there. It’s free to embed on your own site.