Understanding the Coordinate Plane
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.
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.