The point P (−1,2) is rotated to become P′ (2,1). Describe the rotation by degree and direction.

To determine the rotation that transforms the point P (−1, 2) to the point P′ (2, 1), we can analyze the coordinates.

1. **Identifying the rotation:**
- The original point P is at (−1, 2).
- The new point P′ is at (2, 1).

2. **Finding the rotation dimensionally:**
- The transformation from P to P′ involves a change in both the x-coordinate and the y-coordinate.
- We can visualize or calculate the angle needed for this transformation.

3. **Using rotation:**
- Let's consider the origin (0, 0) as the pivot:
- The vector from the origin to P (-1, 2) can be seen as a position vector.
- Applying the standard rotation transformations:
- A 90° counterclockwise rotation converts (x, y) to (-y, x).
- Conversely, a 90° clockwise rotation converts (x, y) to (y, -x).

4. **Verifying rotation:**
- If we rotate point P (−1, 2) by 90° counterclockwise:
- P would transform as follows:
- (−1, 2) → (−2, −1) (90° counterclockwise).
- If we rotate by 90° clockwise, we get:
- (−1, 2) → (2, 1) (90° clockwise).

Thus, we can conclude that to get from P(−1, 2) to P′(2, 1) requires a rotation of **−90°** clockwise.

The correct answer is:
**D. −90° rotation.**

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Thank you for your kind words! I'm glad the explanation helped clarify the rotation of point P to point P′ for you. If you have any more questions about rotations, geometry, or anything else, feel free to ask!