Question

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

−270°
rotation
negative 270 degrees rotation

180°
rotation
180 degrees rotation

90°
rotation

Answer 1

To determine the rotation that moves the point P (−1,2) to P′ (2,1), we can consider the positions of the points.

1. P (−1,2) is located in the second quadrant.
2. P′ (2,1) is located in the first quadrant.

Let's analyze the transformation:

- The original point P (−1, 2) can be represented as being rotated around the origin (0, 0).
- The movement from point P to point P′ involves a change in both x and y coordinates.

To find the angle of rotation, we can look at the change in coordinates:
- From (−1, 2) to (2, 1):
- The x-coordinate changes from −1 to 2 (a change of +3).
- The y-coordinate changes from 2 to 1 (a change of −1).

The rotation that maps from P to P′ corresponds to a 90° rotation counterclockwise.

Thus, the correct response is:
**90° rotation**