2H.1 A rectangle has side lengths a and b, and as shown in Figure 2.32, points P and are selected on the sides of length a so that P Q is parallel to the sides of length b. Show that there exist uniquely determined points X and Y on the sides of length b such that PX + XY+YQ is minimized and show that the minimum possible value for this quantity is 4a2 + b2. b P Figure 2.32