Consider a polygon with the following vertices: (1,1), (1,2), (3,1), and (3,2). We wish to rotate the polygon 60 degrees around its centroid. Set up the matrix equation to achieve this transformation.Make sure you use homogeneous coordinates, and that the sequence of matrices to be applied is shown.Compute the coordinates of the transformed vertices. Draw the original and rotated polygon. Given a 2×2 square with the bottom left corner at (3, 2), show that if a rotation of 45 degrees is performed followed by a translation of +5 along both axes, the final outcome is not the same as applying the operations in reverse order. Set up the matrix equations for both operation sequences and multiply them out to demonstrate that the final position of the square will be different. Show all work Consider the polygon with the following vertices: (1, 1), (6, 2), (9, 4) and (2, 5). We wish to scale it by the factors �! = 2 and �! = 3 while ensuring that the centroid of the object is fixed in location. In order to achieve this would need to compute the coordinate of the centroid Given the centroid, the object would be translated so that its centroid is at (0,0), followed by the scaling. Lastly, the object is translated back to its original location.