Parametric Rectangle

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Over the time interval 0 ≤ t ≤ 1 the 4×2 rectangle centred at the origin transforms into the 2×4 rectangle centred at (4, 4), such that every point (x, y) moves in a straight line at constant speed to its corresponding destination. The diagram is drawn at time T = 0.5 so that, for example, A is halfway between  and .

(a) At one point in the journey of the rectangle, it becomes a line segment. At what time does this happen? How long is the line segment?

(b) At one point in the journey, the rectangle becomes a square. At what time does this happen? What is the side length of the square?