To determine the rotation from point \( P (-1, 2) \) to point \( P' (2, 1) \), we can analyze the transformation.
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Identify the Original and Final Coordinates:
- Original Point \( P (-1, 2) \)
- Rotated Point \( P' (2, 1) \)
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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.
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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.
- To get from \( P \) to \( P' \):
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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.