Understanding the Coordinate Plane

By Mark Ryan

If you need a quick refresher about how the x-y coordinate system works, you’ve come to the right place. Let’s start with the following figure, which shows you the lay of the land of the coordinate plane.

geometry-x-y-plane
The x-y coordinate system.

Here’s the lowdown on the coordinate plane you see in the figure:

  • The horizontal axis, or x-axis, goes from left to right and works exactly like a regular number line. The vertical axis, or y-axis, goes—ready for a shock?—up and down. The two axes intersect at the origin (0, 0).
  • Points are located within the coordinate plane with pairs of coordinates called ordered pairs—like (8, 6) or (–10, 3). The first number, the x-coordinate, tells you how far you go right or left; the second number, the y-coordinate, tells you how far you go up or down. For (–10, 3), for example, you go left 10 and then up 3.
  • Going counterclockwise from the upper-right-hand section of the coordinate plane are quadrants I, II, III, and IV:
    • All points in quadrant I have two positive coordinates, (+, +).
    • In quadrant II, you go left (negative) and then up (positive), so it’s (–, +).
    • In quadrant III, it’s (–, –).
    • In quadrant IV, it’s (+, –).

Because all coordinates in quadrant I are positive, it’s often the easiest quadrant to work in.

  • The Pythagorean Theorem comes up a lot when you’re using the coordinate system because when you go right and then up to plot a point (or left and then down, and so on), you’re tracing along the legs of a right triangle; the segment connecting the origin to the point then becomes the hypotenuse of the right triangle. In the figure, you can see the 6-8-10 right triangle in quadrant I.