Question

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

-270 degree rotation
-270 degree rotation

180 degree rotation
180 degree rotation

90 degree rotation
90 degree rotation

270 degree rotation

Answer 1

To determine the rotation from point \( P (-1, 2) \) to point \( P' (2, 1) \), we can analyze the transformation.

1. **Identify the Original and Final Coordinates:**
- Original Point \( P (-1, 2) \)
- Rotated Point \( P' (2, 1) \)

2. **Visualizing the Rotation:**
- The center of rotation is not defined here, so we can test it around the origin (0,0).
- We can then determine how to get from \( P \) to \( P' \) by using circular rotation.

3. **Calculating the required parameters:**
- To get from \( P \) to \( P' \):
- The vector from \( P \) to the origin is (-1, 2), and the vector from the origin to \( P' \) is (2, 1).
- Now we can determine the angle of rotation needed:
- In a coordinate plane, a 90-degree rotation counterclockwise takes \((x, y)\) to \((-y, x)\).
- Testing a 90-degree rotation: if you take the point \((-1, 2)\):
- A 90-degree counterclockwise rotation would result in \((-2, -1)\), not our target.
- A 90-degree clockwise rotation takes \((x, y)\) to \((y, -x)\). If we apply this to \((-1, 2)\):
- \((-1, 2)\) becomes \((2, 1)\), which matches our point.

4. **Determining the Rotation:**
- Since a clockwise rotation of 90 degrees moves \( (-1, 2) \) to \( (2, 1) \), the correct description of this rotation is a **90 degree clockwise rotation**.

Therefore, the answer is: **90 degree rotation**.