Solved: The semicircle depicted as the original figure in Exercise [2 is to be

Chapter 6, Problem 13

(choose chapter or problem)

The semicircle depicted as the original figure in Exercise [2 is to be transfonned by a rotation of90" counterclockwise about the point ([. [). (a) Sketch the image of the semicircle. 4 r,,--c, -',--r ,,--c, -',---; _~_.I. __ ~_.J __ I __ I I I I I , _L_l._.l __ J_.J __ ' __ I I I I I , I I I I I I -,-,-T- ,-,--,-- o r-~-- ' --I- --~' --i I I I I I I - [ - "" -'--1"- --1 - "--'-- I I I I I I - 2 -~-+- --t-~--I-- I I I I I I - 3 -~_~_.I. __ ~_~ _ _I __ I I I I I I 4' ~4-C3c"2~7COC-7-"2--'3~4 14. (b) Using transform1tions. we must first translate the semicircle to the origin. rotate it. and then translate it back to its original position. Determine the 3 x 3 matrix M in homogeneous fonn that will perfonn this tmnsfonnation. (c) Verify that your matrix M is correct by computing the image of the endpoints of the horizontal diameter of the semicircle.