To determine the rotation that transforms the point P (−1, 2) into P′ (2, 1), we can analyze the coordinates and their positions on the Cartesian plane.
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Plot the points:
- P (−1, 2) is located in the second quadrant.
- P′ (2, 1) is located in the first quadrant.
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Calculate the angle of rotation:
- From point P to P′, we can observe that the x-coordinate of P changes from -1 to 2 (a change of +3), and the y-coordinate changes from 2 to 1 (a change of -1).
- This suggests a rotation to the right (clockwise).
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Find the rotation:
- The original point (−1, 2) can be visualized as being 180° away from the x-axis if we were to rotate it:
- A -90° rotation will move the point from the second quadrant to the fourth quadrant.
- A -270° (or +90°) rotation moves it from the second quadrant to the first quadrant.
- To verify, we can use the formula for rotation. A point (x, y) rotated by -90° (which corresponds to a clockwise rotation) becomes (y, -x):
- For P (−1, 2): After a -90° rotation, it becomes (2, 1), which is exactly P′.
- The original point (−1, 2) can be visualized as being 180° away from the x-axis if we were to rotate it:
Thus, the rotation that transforms point P (−1, 2) into P′ (2, 1) is −90°.
The answer is B. -90°.
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