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

To determine the rotation of point P (−1, 2) to P′ (2, 1), we can analyze the transformation geometrically.

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

To find the center of rotation, we first calculate the midpoint of the line segment connecting the points P and P′:

\[
\text{Midpoint} = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) = \left( \frac{-1 + 2}{2}, \frac{2 + 1}{2} \right) = \left( \frac{1}{2}, \frac{3}{2} \right)
\]

Next, we can visualize or calculate how the point has moved. The change in coordinates is as follows:

\[
\Delta x = 2 - (-1) = 3
\]
\[
\Delta y = 1 - 2 = -1
\]

The movement from P to P′ suggests a rotation. Considering the standard rotations in the counterclockwise direction:

- A 90° rotation counterclockwise would rotate (x, y) to (-y, x). Applying this to P (−1, 2) gives:
\[
(−2, −1)
\]
which does not match P′.

- A 180° rotation would give:
\[
(1, -2)
\]
which also does not match.

- A −90° rotation (which is equivalent to 270° rotation in the clockwise direction) would give:
\[
(2, −1)
\]
which again does not match.

Testing a −90° rotation (or 270° clockwise), we can also rotate the point correctly, leading into the conclusion:

Only with further transformation or possibly calculations into quadrant adjustments can we arrive precisely at P′ without additional translational adjustments. Given our options and simplifying transformations, it appears rotational movement from the origin tracing axes is leading closer toward a

The correct response based on transformations and available choices is:
- **−90° rotation** (which corresponds to a 270° clockwise rotation).