You work for a computer graphics company and you are the chief developer of visual effects and computer animated applications.You have beentasked with the writing of a computerprogram that manipulate s two-dimensional objectsthat are specified by a collection of cornerpoints.
(a) Find the 2 x 2 transformation matrix A that scales agiven object by a factor of ? in the horizontal direction(x-axis) and by a factor of ? inthe vertical direction (y-axis).
(b) Find the 2 x 2 transformation matrix Bthat rotates the object about the origin by anangle of ? in the clockwise sense.
(c) LetC1 be the 2 x 2 matrix that represents the combined transformation "first scale, thenrotate". Let C2 bethe matrix thatperformsthe combined transformation in reverse order. Find C1 andC2.
(d) Explain why C1? C2.
(e) Find the 2 x 2 matrices that undo the operations performed by C1 and C2.
(t) A triangle with verticesat (0, 0), (4, 0), and (0, 1) undergoes scaling by a factor of 0.5 in the horizontal direction and by a factor of 3 inthe vertical direction, followedby a clockwise rotation of 90° about the origin. Determinethe new coordinates of the triangle as a result of thistransformation.