Square ABCD was translated using the rule (x, y) → (x – 4, y + 15) to form A'B'C'D'. What are the coordinates of point D in the pre-image if the coordinates of point D’ in the image are (9, –8)?

The translation changes a pre-image point (x, y) to (x − 4, y + 15). To find the pre-image from D′ = (9, −8), reverse those changes: add 4 to the x-coordinate and subtract 15 from the y-coordinate. Thus D = (9 + 4, −8 − 15) = (13, −23), choice A.

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