Final answer:
Under a dilation of scale factor centered at (3,1), the shape of AB remains the same.
Step-by-step explanation:
In a dilation, the shape of a figure changes proportionally to the scale factor. If the scale factor is greater than 1, the shape expands. If the scale factor is between 0 and 1, the shape shrinks. Since the question doesn't provide information about the scale factor, we can't determine whether the shape of AB becomes A'B' by expanding or shrinking. Therefore, the answer is (a) it remains the same.