o Problem 1. (4 points) The quadrilateral shown undergoes 2-D geometric transformation and 1s shown in the sketch in 1ts onginal position. The coordinates of the vertices are given as (X.y) below and labeled. The quadrilateral is first uniformly scaled about the point A to be 1/4 of its onginal size, then translated 3 units in x-direction and (4) units in y-direction and then finally rotated about point C by 30 CW. Determine the final transformed coordinates of the vertices: A B, C,and D'. Initial Coordinates: A(1.4), B(2.1), C(3.4), and D{2,5) IS Given Coordinates A ( 2 , 3) D ( 4 , 8 ) [ A - 2 4 6 4 2 B ( 4 , 2 ) E ( 2, 7 ) 3 2 5 87 C ( 6, 5 ) Operations performed : 1) Translation in ty direction by 4 units ( Ti ) 2) Rotated about the 2 axis 45 CW about the coigin ( R ) IW Scaled about the origin to half the original size (S. ) T, = O O 4 Since Rotation is (W 9= -45R , = cos ( - 45 ) - Sin ( - 45 ) O Sin (-45) Cos (-45) O - Cos ( 450 ) Sin (450 ) 0 - Sin (459) cos ( 459 ) O O S 1/ 12 1/52 o 1/ 52 0 O S,= 1/2 0 0 0 /2 0 LO O so final Coordinates [A] = [s, ] [ R. ] [T . ] [A ]\f