To determine the rotation that transforms the point P (−1, 2) into P′ (2, 1), we can first look at the changes in the coordinates:
The original point P is at (-1, 2), and after the transformation, P' is at (2, 1).
To rotate the point, we consider the change in both the x and y coordinates.
The point P is in the second quadrant, and P' is in the first quadrant.
To find the angle of rotation:
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Translate the origin: Shift the point to the origin by adding (1, -2) to both points.
- P becomes (0, 0)
- P′ becomes (3, -1)
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Determine the angle of rotation: You can visualize or calculate angles based on the quadrants changes:
- The y-coordinate decreases from 2 to 1 while x-coordinate increases from -1 to 2.
- This suggests a counter-clockwise rotation.
Calculating the angle directly:
- Original point P (-1, 2) and Target point P' (2, 1).
- To find the angle, consider the change in coordinates. Plotting these points would show a counter-clockwise movement.
We can use geometry to conclude:
- The rotation that fits this transformation is 90° counter-clockwise, which can also be described as −270° (since rotating 270° clockwise is equivalent to 90° counter-clockwise).
Thus, the rotation that describes P to P′ is: 90° rotation (90 degrees rotation) or −270° rotation (negative 270 degrees rotation).
Therefore, either "90° rotation" or "−270° rotation" is correct, but the most direct answer would be 90° rotation.