Geometry Essentials For Dummies

Chapter 11

Coordinate Geometry

IN THIS CHAPTER

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

Calculating the distance between two points

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), ...