Chapter 11

Coordinate Geometry


Bullet Finding a line’s slope and a segment’s midpoint

Bullet Calculating the distance between two points

Bullet Working with equations of lines and circles

In this chapter, you investigate the same sorts of things you see in previous chapters: perpendicular lines, right triangles, circles, perimeter, the diagonals of quadrilaterals, and so on. What’s new about this chapter is that these familiar geometric objects are placed in the x-y coordinate system and then analyzed with algebra.

The Coordinate Plane

If you need a quick refresher about how the x-y coordinate system works, no worries. Check out Figure 11-1.

  • 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.
  • Going counterclockwise from the upper-right-hand section of the coordinate plane are quadrants I, II, III, IV.
  • 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), ...

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