Question

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

−90°
rotation
negative 90 degrees rotation

90°
rotation
90 degrees rotation

180°
rotation
180 degrees rotation

−270°
rotation

Answer 1

To determine the degree and direction of the rotation that transforms point \( P (-1, 2) \) to point \( P' (2, 1) \), we can analyze their coordinates.

1. **Identifying the center of rotation (assuming it's around the origin)**:

- The original point \( P (-1, 2) \) can be visualized on the Cartesian plane.
- The new point \( P' (2, 1) \) should also be visualized.

2. **Calculating the rotation**:

Let's check the coordinates:
- \( P \) is at \( (-1, 2) \).
- \( P' \) is at \( (2, 1) \).

To understand the rotation, we look at the movement of \( P \) to \( P' \). The transformation can be deduced as follows:
- Starting at \( P (-1, 2) \), if we rotate \( -90^\circ\) (which is a clockwise rotation):
1. The \( x \)-coordinate will become the negative of the original \( y \)-coordinate, and the \( y \)-coordinate will become the original \( x \)-coordinate.
2. So \( (-1, 2) \) becomes \( (-2, -1) \).

This transformation doesn't match \( P' \). Let’s check the logic again using graphing or a coordinate transformation method.

**Checking against a rotation matrix for -90 degrees:**
- \( (x', y') = (y, -x) \)

From \( P(-1, 2) \):
- New coordinates after -90 degrees rotation should be \( (2, 1) \), which matches \( P' \).

3. **Conclusion**:

The correct description of the rotation that takes point \( P (-1, 2) \) to point \( P' (2, 1) \) is a **-90° rotation**. Hence, the answer is:

**−90° rotation**