8.5 Transformational Geometry, Symmetry, and Tessellations 503 Solution The reflection of triangle ABC will be called A BC. ′ ′ ′ To determine the position of the reflection, we first examine vertex A in Fig. 8.49. Notice that vertex A is 2 units to the right of line l. Thus, in the reflected triangle A BC , ′ ′ ′ vertex A′ must also be 2 units away from, but to the left of, reflection line l (see Fig. 8.50). Next, notice that vertex B is 6 units to the right of line l. Thus, in the reflected triangle A BC , ′ ′ ′ vertex B′ must also be 6 units away from, but to the left of, reflection line l. Next, notice that vertex C is 6 units to the right of line l. Thus, in the reflected triangle A BC , ′ ′ ′ vertex C′ must also be 6 units away from, but to the left of, reflection line l. Figure 8.50 shows vertices A B, , ′ ′ and C.′ Finally, we draw line segments between vertices A′ and B ,′ between B′ and C ,′ and between A′ and C′ to form the sides of the reflection triangle A B C , ′ ′ ′ as illustrated in Fig. 8.50. A A9 B B9 C C9 l 6 units 6 units 6 units 6 units 2 units 2 units Figure 8.50 7 In Example 1, the reflection line did not intersect the figure being reflected. We will now study an example in which the reflection line goes directly through the figure to be reflected. Example 2 Reflection of a Hexagon Construct the reflection of hexagon ABCDEF, shown in Fig. 8.51, about reflection line l. Solution From Fig. 8.51 we see that vertex A in hexagon ABCDEF is 2 units to the left of reflection line l. Thus, vertex A′ in the reflected hexagon will be 2 units to the right of l (see Fig. 8.52). Notice that vertex A′ of the reflected hexagon is in the same location as vertex B of hexagon ABCDEF in Fig. 8.51. A B D E F C l Figure 8.51 B9 A9 E9 D9 C9 F9 l Figure 8.52 Now try Exercise 9
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