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

(1 point)
0-270°
rotation
• 180° rotation
• -90° rotation
• 90° rotation

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
1 month ago

To determine the rotation of point P (-1, 2) to P' (2, 1), we can analyze the change in coordinates.

1. **Identify the original and new points**:
- P = (-1, 2)
- P' = (2, 1)

2. **Calculate the movement**:
- The x-coordinate changes from -1 to 2 (which is an increase of 3).
- The y-coordinate changes from 2 to 1 (which is a decrease of 1).

3. **Visualize the rotation**:
- We can visualize this transformation in a coordinate system.
- The point P is in the second quadrant (where x is negative and y is positive).
- The point P' is in the first quadrant (where both x and y are positive).

4. **Identify the rotation direction**:
- A 90° rotation counterclockwise (or -270°) moves a point (x, y) to (-y, x).
- A 90° rotation clockwise (or 270°) moves a point (x, y) to (y, -x).
- A 180° rotation moves a point (x, y) to (-x, -y).

5. **Check the transformation**:
- If we apply a 90° rotation clockwise to point P (-1, 2):
- The new coordinates would be (2, 1), which matches point P'.

Thus, the correct description of the rotation is:
**90° rotation clockwise (or -270° rotation counterclockwise)**.

Since the options provided include "90° rotation," that is the answer.