Question

The point P (4,2) is rotate to become P'(-2,4). Describe the rotation by degree and direction.(1 point)
Responses

90°rotation
90 degreesrotation

−90°rotation
negative 90 degreesrotation

−270°rotation
negative 270 degreesrotation

180°rotation

Answer 1

To determine the rotation that takes point \( P(4, 2) \) to point \( P'(-2, 4) \), we can analyze the transformation.

1. **Visualize the Points**:
- Point \( P(4, 2) \) is located in the first quadrant.
- Point \( P'(-2, 4) \) is located in the second quadrant.

2. **Calculate the Angle of Rotation**:
- Estimate the angle of rotation from point \( P \) to point \( P' \).

**Using coordinates**:
- To rotate a point \( (x, y) \) counterclockwise by 90 degrees, the new coordinates will be \( (-y, x) \).
- For a 90 degrees push of rotation:
- \( (4, 2) \) would transform to \( (-2, 4) \), which matches \( P'(-2, 4) \).

Therefore, \( P \) has been rotated counterclockwise by 90 degrees to reach \( P' \).

3. **Conclusion**:

Based on the transformation, the answer is:
- **90° rotation** (counterclockwise).

So the response is:
**90° rotation**.