The point P (-1,2) is rotated to become P′

Question

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



(1 point)
Responses

90° rotation
90° rotation

−270° rotation
−270° rotation

−90° rotation
−90° rotation

180° rotation

Answer 1

To determine the rotation that maps point P (-1, 2) to point P' (2, 1), we can analyze the coordinates.

First, we can find the vector from P to P':

• Starting point P = (-1, 2)
• End point P' = (2, 1)

Calculating the vector: Δx = 2 - (-1) = 3 Δy = 1 - 2 = -1

Next, we can think about the typical rotations:

• A 90° rotation clockwise gives us a transformation from (x, y) to (y, -x).
• A 90° rotation counterclockwise gives us (x, y) to (-y, x).
• A 180° rotation transforms (x, y) to (-x, -y).
• A −90° rotation (or 270° rotation clockwise) transforms (x, y) to (-y, x) (same as 90° counterclockwise).

To find out the rotation type:

1. Starting with the 90° Clockwise Rotation:

   • From P (-1, 2): (2, 1) matches.

2. Check the vector: The initial vector is (3, -1), which corresponds to a movement down and right. This is a clockwise rotation.

Thus, the movement from P (-1, 2) to P' (2, 1) represents a 90° clockwise rotation.

Therefore, the correct response is:

90° rotation.