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

Question

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



(1 point)
Responses

180° rotation
180° rotation

90° rotation
90° rotation

−270° rotation
−270° rotation

−90° rotation

Answer 1

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

1. Initial Position: P (-1, 2)
2. Final Position: P' (2, 1)

Now, let’s examine the transformation:

• The x-coordinate changes from -1 to 2, which is an increase of 3.
• The y-coordinate changes from 2 to 1, which is a decrease of 1.

The transformation can be visualized by plotting these points on a Cartesian plane.

Next, we'll check for potential rotations around the origin:

180° Rotation

A 180° rotation around the origin switches the signs of both coordinates:

• P (x, y) -> P' (-x, -y)

Applying to P:

• P( -1, 2 ) rotates to P' (1, -2), which is incorrect.

90° Rotation

A 90° rotation around the origin would transform the coordinates as follows:

• P (x, y) -> P' (-y, x)

Applying to P:

• P( -1, 2 ) rotates to ( -2, -1), which is incorrect.

-90° Rotation

A -90° rotation (or a clockwise rotation) transforms the coordinates as follows:

• P (x, y) -> P' (y, -x)

Applying to P:

• P( -1, 2 ) rotates to ( 2, 1), which matches P'.

−270° Rotation

A -270° rotation (or a +90° rotation) would be:

• P (x, y) -> P' (-y, x)

Applying to P:

• P( -1, 2 ) rotates to ( -2, -1), which is incorrect.

Based on the analysis above, the correct transformation is a −90° rotation.

So the answer is −90° rotation.