Consider the rectangle with vertices (3, 2), (7, 2), (7, 4), and (3, 4). a. Plot the

Chapter 11, Problem 1

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Consider the rectangle with vertices (3, 2), (7, 2), (7, 4), and (3, 4). a. Plot the rectangle on graph paper. Write a transformation matrix [A] to rotate this rectangle counterclockwise 20, dilate it by a factor of 0.9, and translate it 6 units in the x-direction and 1 unit in the y-direction. Write a matrix [M] for the pre-image rectangle, apply the transformation, and plot the image on graph paper. b. Enter the matrices on your grapher and perform the transformation in part a iteratively, plotting the images using the program from in Section 11-3. Sketch the path followed by the images. To what fixed point do the images seem to be attracted? c. Find the approximate location of the fixed point numerically by finding [A]100[M]. Does it agree with the answer you found graphically in part b? d. Find the location of the fixed point algebraically. Show that your answer agrees with the answers you found graphically and numerically in parts b and c.