Question

The point P (−1,2) is rotated to become P′ (2,1) . Describe the rotation by degree and direction.(1 point) Responses 90° counter-clockwise rotation 90° counter-clockwise rotation 270° clockwise rotation 270° clockwise rotation 90° clockwise rotation 90° clockwise rotation 180° counter-clockwise rotation

Answer 1

To determine the rotation from point P (−1,2) to point P′ (2,1), let's analyze the transformation.

1. The original point P is located at (-1, 2).
2. The target point P′ is located at (2, 1).

To understand the rotation, consider the following steps:

- The coordinates of point P (-1, 2) means it is to the left of the y-axis and above the x-axis.
- The coordinates of point P′ (2, 1) means it is to the right of the y-axis and below the point (-1, 2).

Now, if we visualize or sketch the transformation:

- A 90° counter-clockwise rotation around the origin would change the coordinates of P as follows:
- New x-coordinate = original y-coordinate
- New y-coordinate = -original x-coordinate
- Thus:
- For point P (-1, 2):
- New x-coordinate = 2 (original y-coordinate)
- New y-coordinate = -(-1) = 1 (negation of original x-coordinate)
- Hence, the new point after a 90° counter-clockwise rotation would be (2, 1), which matches P′.

Therefore, the transformation from P to P′ is a **90° counter-clockwise rotation**.