6-8 Applying Coordinate Geometry

Objective

To name coordinates of special figures by using their properties

Image Long Description

In the Solve It, you found coordinates of a point and named it using numbers for the x- and y-coordinates. In this lesson, you will learn to use variables for the coordinates.

Essential Understanding You can use variables to name the coordinates of a figure. This allows you to show that relationships are true for a general case.

In Chapter 5, you learned about the segment joining the midpoints of two sides of a triangle. Here are three possible ways to place a triangle and its midsegment.

Figure 1

Figure 2

Figure 3

Figure 1 does not use the axes, so it requires more variables. Figures 2 and 3 have good placement. In Figure 2, the midpoint coordinates are M ( a 2 , b 2 ) m open , eh over 2 , comma , b over 2 , close and N ( a + c 2 , b 2 ) . n open . fraction eh plus c , over 2 end fraction . comma , b over 2 , close .

In Figure 3, the coordinates are M( − a , negative eh comma b) and N(c, b). You can see that Figure 3 is the easiest to work with.

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