Chapter 6 (Please Include all the questions answered as well as chapters correctly)

10. In Fig. 11-44, R' is the image of R under a reflection. (a) Find the axis of reflection. (b) Find the image of the shaded arrow under the reflection. R' R Figure 11-44H D C B LE G F Figure 11-47 14. In Fig. 11-47, indicate which point is (a) the image of C under a 90 counterclockwise rotation with rotocenter B. (b) the image of F under a 60 clockwise rotation with rotocenter A. (c) the image of F under a 120 clockwise rotation with rotocenter B. (d) the image of / under a 90 clockwise rotation with roto- center H.17. In Fig. 11-48, a rotation moves B to B' and C to C'. (a) Find the rotocenter. (b) Find the image of triangle ABC under the rotation.\f20. In Fig. 11-51, a rotation moves ( to O' and R to R'. (a) Find the rotocenter. (b) Find the angle of rotation. (c) Find the image of quadrilateral PORS under the rotation. R' S P R O Figure 11-5121. In Fig. 11-52, find the image of triangle ABC under a 60 clockwise rotation with rotocenter O. B C Figure 11-5222. In Fig. 11-53, find the image of ABCD under a 60 counter- clockwise rotation with rotocenter O. B Figure 11-5330. Given a glide reflection with vector v and axis / as shown in Fig. 11-61, find the image of the quadrilateral ABCD under the glide reflection. M B C D Figure 11-6136. In Fig. 11-67, P' is the image of P and O' is the image of @ under a glide reflection. Find the image of the shaded figure under the glide reflection. P Figure 11-676. In Fig. 11-40, / is the axis of reflection. (a) Find the image of P under the reflection. (b) Find the image of the parallelogram PORS under the reflection. P S R Figure 11-4010. Consider the graph in Fig. 6-26. (a) Find all the Hamilton circuits in the graph, using B as the starting/ending vertex. (Hint: There are five Hamil- ton circuits and another five that are reversals of the first five.) (b) Find the four Hamilton paths that start at B and do not come from "broken" Hamilton circuits (i.e., cannot be closed into a Hamilton circuit). B C A Fa E Figure 6-2616. Explain why the graph shown in Fig. 6-32 has neither Ham- ilton circuits nor Hamilton paths. A B E Da OC G Figure 6-3228. Find an optimal tour for the TSP given in Fig. 6-38, and give its cost. A 80 40 30 60 D 20. C o B 25 Figure 6-3836. A space mission is scheduled to visit the moons Callisto (C). Ganymede (G). Io (/). Mimas (M), and Titan (7) to collect rock samples at each and then return to Earth (F). The travel times (in years) are given in the weighted graph shown in Fig. 6-44. (Nore: This is the interplanetary TSP discussed in Example 6.11.) (a) Find the nearest-neighbor tour with starting vertex E. Give the total travel time of this tour. (b) Find the nearest-neighbor tour with starting vertex 7. Write the tour as it would be traveled by an expedition starting and ending at E. Give the total travel time of this tour. 5.1 47 5.2 0.6 8.2 5.9 LT 3.6 8.1 1.1 3.1 15 3.2 5.6 Figure 6-444. Find all possible Hamilton circuits in the graph in Fig. 6-22. Write your answers using A as the starting/ending vertex. A B D Figure 6-22