Let P be a point with coordinates (a, b), and assume that c and d are positive numbers. (The condition that c and d are positive isn’t really necessary in this problem, but it will help you to visualize things.)
(a) Translate the point P by c units in the x-direction to obtain a point Q, then translate Q by d units in the y-direction to obtain a point R. What are the coordinates of the point R?
(b) Translate the point P by d units in the y-direction to obtain a point S, then translate S by c units in the x-direction to obtain a point T. What are the coordinates of the point T?
(c) Compare your answers for parts (a) and (b). What have you demonstrated? (Answer in complete sentences.)
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