506 CHAPTER 8 Geometry Rotations The next rigid motion we will discuss is rotation. To help visualize a rotation, examine Fig. 8.59, which shows right triangle ABC and point P, about which right triangle ABC is to be rotated. Solution The translated figure will be a square of the same size and shape as square ABCD. We notice that the translation vector, v, points 6 units downward and 3 units to the right. To determine the location of vertex A′ of the translated square, start at vertex A of square ABCD and move down 6 units and to the right 3 units. We label this vertex A′ (see Fig. 8.58a). We determine vertices B C, , ′ ′ and D′ in a similar manner by moving down 6 units and to the right 3 units from vertices B C, , and D, respectively. Figure 8.58(b) shows square ABCD and the translated square A BC D. ′ ′ ′ ′ Notice in Fig. 8.58(b) that every point on square A BC D ′ ′ ′ ′ is 6 units down and 3 units to the right of its corresponding point on square ABCD. (a) v A B C D A9 B9 C9 D9 3 units to the right 6 units downward Figure 8.58 (b) A B C D A9 B9 C9 D9 7 Now try Exercise 19 A B C P Figure 8.59 Imagine that Figure 8.59 was printed on a page that was attached to a bulletin board with a single pin through point P. Next imagine rotating the page 90° in the counterclockwise direction. The triangle would now appear as triangle A BC ′ ′ ′ shown in Fig. 8.60. Next, imagine rotating the original triangle 180° in a counterclockwise direction. The triangle would now appear as triangle A B C ″ ″ ″ shown in Fig. 8.61. C9 B9 A9 A B C P Figure 8.60 A0 B0 C0 A B C P Figure 8.61
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