The point P (-1,2) is rotated to become P′

Question

(2,1). Describe the rotation by degree and direction.



(1 point)
Responses

−90° rotation
−90° rotation

180° rotation
180° rotation

90° rotation
90° rotation

−270° rotation

Answer 1

To determine the rotation necessary to transform point P (-1, 2) into point P′ (2, 1), we can analyze the original and final coordinates.

1. Identify the coordinates:

   • P (-1, 2)
   • P′ (2, 1)

2. Determine the differences:

   • The x-coordinate changed from -1 to 2, which is an increase of 3.
   • The y-coordinate changed from 2 to 1, which is a decrease of 1.

3. Visualize the rotation:

   • A 90° rotation counterclockwise (or -270°) around the origin specifically changes coordinates from (x, y) to (-y, x):
     • For P (-1, 2), a 90° rotation would yield (–2, -1), which does not match P′.
   • A 90° rotation clockwise (or +270°) changes coordinates from (x, y) to (y, -x):
     • For P (-1, 2), this would yield (2, 1), which exactly matches P′.

Therefore, the proper transformation from P to P′ is a 90° clockwise rotation.

The correct response is:

90° rotation