To determine the rotation that transforms point P (−1, 2) to P′ (2, 1), we can analyze the change in position of the point.
- Start with the original point P (−1, 2).
- The new point P′ (2, 1) has coordinates where the x-coordinate increases from −1 to 2 (a change of +3) and the y-coordinate decreases from 2 to 1 (a change of −1).
Next, we review the rotation transformations:
- A 90° clockwise rotation will transform P (−1, 2) to a point. To find that point, we can use the following transformation:
- If a point (x, y) is rotated 90° clockwise, the new coordinates (x', y') will be (y, -x).
- Here, (−1, 2) becomes (2, 1), which matches P′.
Thus, the rotation that transforms P to P′ is:
90° rotation clockwise.
So, among the given options, the correct response is:
90° rotation or 90 degrees rotation.