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.