502 CHAPTER 8 Geometry Definition: Reflection A reflection is a rigid motion that moves a geometric figure to a new position such that the figure in the new position is a mirror image of the figure in the starting position. In two dimensions, the figure and its mirror image are equidistant from a line called the reflection line or the axis of reflection. Figure 8.48 shows trapezoid ABCD, a reflection line l, and the reflected trapezoid A BC D. ′ ′ ′ ′ Notice that vertex A is 6 units to the left of reflection line l and that vertex A′ is 6 units to the right of reflection line l. Next notice that vertex B is 2 units to the left of l and that vertex B′ is 2 units to the right of l. A similar relationship holds true for vertices C and C′ and for vertices D and D.′ It is important to see that the trapezoid is not simply moved to the other side of the reflection line, but instead it is reflected. Notice in the trapezoid ABCD that the longer base BC is on the right side of the trapezoid, but in the reflected trapezoid A BC D ′ ′ ′ ′ the longer base BC′ ′ is on the left side of the trapezoid. Finally, notice the colors of the sides of the two trapezoids. Side AB in trapezoid ABCD and side A B′ ′ in the reflected trapezoid are both blue. Side BC and side BC′ ′ are both red, sides CD and C D′ ′ are both brown, and sides DA and D A′ ′ are both green. In this section, we will occasionally use such color coding to help you visualize the effect of a rigid transformation on a figure. A D B B9 A9 D9 C9 C Reflection line l 6 units 6 units Figure 8.48 Example 1 Reflection of a Triangle Construct the reflection of triangle ABC, shown in Fig. 8.49, about reflection line l. A B C l Figure 8.49
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