Represent the following transformations using matrices and vectors. In each case, apply the transformations to A(0,0), B(1,0), C(1,1), and D(0,1) to find their images A’, B’, C’ and D’ and draw your result:
(a) Rotation about the origin through 120?.
(b) Translation by (−4, 1).
(c) Reflection in the x-axis.
(d) Scaling in the y-direction by 5.
(e) Rotation through 120? about the origin followed by a translation by (−2, 3).
(f) Translation by (−1, 3) followed by rotation through 120? about the origin.
(g) Rotation through 120? about the origin followed by scaling by 5 in the y-direction.
(h) Reflection in the line y = x.
(i) Scaling along a line at a 30? angle to the x-axis, by a factor of 4.
(k) Find inverse transformations for those given in parts (a),(b),(c),(e),(g), and (i) and check in each case that the inverse transformation returns A’, B’, C’, and D’ to A,B,C,D.