The point P (−1,2)

Question

𝑃

(
−
1
,
2
)
is rotated to become P′ (2,1)
𝑃
′

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

180°
180
°
rotation
180 degrees rotation

90°
90
°
rotation
90 degrees rotation

−270°
−
270
°
rotation
negative 270 degrees rotation

−90°
−
90
°
rotation

Answer 1

To determine the rotation that transforms the point P (-1, 2) into P' (2, 1), we can analyze the change in coordinates.

1. The original point P is located at (-1, 2).
2. The new point P' is at (2, 1).

To visualize the rotation, we can find the center of rotation. For a 90° rotation, we would typically move the point around the origin (0, 0). Let's check if that transformation applies here:

• A 90° rotation counterclockwise around the origin would transform the point (x, y) to (-y, x).

• For P (-1, 2):

  • The expected transformation for a 90° counterclockwise rotation is (−2, -1), not (2, 1).

• For a 180° rotation around the origin, the transformation (x, y) goes to (−x, −y).

• For P (-1, 2):

  • The expected transformation for a 180° rotation is (1, −2), not (2, 1).

• A -90° (or 270°) rotation would transform (x, y) to (y, -x).

• For P (-1, 2):

  • That transformation would result in (2, 1). This matches P' (2, 1).

Thus, the correct answer is:

• −90° rotation (or negative 90 degrees rotation).