Question

the point P (-1,2) is rotated to become P' (2,1). Describe the rotation by degree and direction.
a. -270 rotation
b. 180 rotation
c. 90 rotation
d. -90 rotation

Answer 1

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

1. **Original Point \( P(-1, 2) \)**:
- \( x = -1 \)
- \( y = 2 \)

2. **New Point \( P'(2, 1) \)**:
- \( x' = 2 \)
- \( y' = 1 \)

### Calculation of Rotation:

We can use the following transformation formulas to investigate the effect of various rotations on the coordinates.

- A **90-degree rotation counterclockwise** about the origin transforms \( (x, y) \) to \( (-y, x) \).
- A **90-degree rotation clockwise** (or -90 degrees counterclockwise) transforms \( (x, y) \) to \( (y, -x) \).
- A **180-degree rotation** transforms \( (x, y) \) to \( (-x, -y) \).
- A **270-degree rotation counterclockwise** (or -90 degrees clockwise) transforms \( (x, y) \) to \( (y, -x) \).

### Checking Each Option:
1. **Option a: -270 degrees** (equivalently 90 degrees clockwise)
- \( (-1, 2) \to (2, 1) \) (Correct)

2. **Option b: 180 degrees**
- \( (-1, 2) \to (1, -2) \) (Incorrect)

3. **Option c: 90 degrees**
- \( (-1, 2) \to (-2, -1) \) (Incorrect)

4. **Option d: -90 degrees**
- \( (-1, 2) \to (2, -1) \) (Incorrect)

Given the calculations, the rotation that takes point \( P(-1, 2) \) to point \( P'(2, 1) \) is a **-270 degree rotation (or 90 degrees clockwise)**.

### Conclusion:
The correct answer is:
**a. -270 rotation**