Final answer:
The question seeks to determine the coordinates post-rotation about the point (2, 1). The rotation involves translating, rotating by using standard formulas, and translating back. The answer choices must match these steps, but without initial positions, the correct endpoints cannot be determined.
Step-by-step explanation:
The question involves finding the coordinates of the endpoints of a segment after a counterclockwise rotation of 90° about a point. To do so, we use the standard rotation transformation formulas for a 90° counterclockwise rotation about the origin:
However, since our rotation is about the point (2, 1), we have to adjust our coordinates to treat (2, 1) as the origin. First, we translate points P' and Q' such that (2, 1) becomes the new origin. Then, we apply the rotation formulas and finally translate the points back to their original position based of the (2, 1) origin.
Example: If we have P'(-1,-6), the translation adjusted coordinates would be (-3, -7). We apply the rotation to get the rotated coordinates (7, -3). Then we translate back by adding (2, 1) to get the final rotated position (9, -2).
Note that the answer choice must reflect the correct rotated and translated positions of both P' and Q'. Without the specific initial coordinates for P' and Q', we cannot confidently determine the correct answer choice.