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

Question

A. −270° rotation
B. 180° rotation
C. 90° rotation
D. −90° rotation

Answer 1

To determine the rotation that transforms the point P (−1, 2) to the point P′ (2, 1), we can analyze the coordinates.

1. Identifying the rotation:

   • The original point P is at (−1, 2).
   • The new point P′ is at (2, 1).

2. Finding the rotation dimensionally:

   • The transformation from P to P′ involves a change in both the x-coordinate and the y-coordinate.
   • We can visualize or calculate the angle needed for this transformation.

3. Using rotation:

   • Let's consider the origin (0, 0) as the pivot:
   • The vector from the origin to P (-1, 2) can be seen as a position vector.
   • Applying the standard rotation transformations:
     • A 90° counterclockwise rotation converts (x, y) to (-y, x).
     • Conversely, a 90° clockwise rotation converts (x, y) to (y, -x).

4. Verifying rotation:

   • If we rotate point P (−1, 2) by 90° counterclockwise:
     • P would transform as follows:
     • (−1, 2) → (−2, −1) (90° counterclockwise).
   • If we rotate by 90° clockwise, we get:
     • (−1, 2) → (2, 1) (90° clockwise).

Thus, we can conclude that to get from P(−1, 2) to P′(2, 1) requires a rotation of −90° clockwise.

The correct answer is: D. −90° rotation.

Answer 2

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Answer 3

Thank you for your kind words! I'm glad the explanation helped clarify the rotation of point P to point P′ for you. If you have any more questions about rotations, geometry, or anything else, feel free to ask!