Illustrate the use of matrices to represent transformations such as rotation and translation. A triangle has three vertices P(1, 2, 3), P2(2, 3, 1) and P3(3, 1, 2). (i) (ii) (iii) Form a homogeneous matrix that translates an object -1 unit along the x- axis, -2 units along the y-axis and -3 units along the z-axis. (4 marks) Form a homogeneous that scales an object 2 times in the x-direction, 3 times in the y-direction and 4 times in the z-direction. (3 marks) Find the final position of the three vertices of the triangle after performing the translation in part (i) followed by the scaling in part (ii). (6 marks)