the point P (-1,2) is rotated to become P' (2,1). Describe the rotation by degree and direction.

Question

a. -270 rotation
b. 180 rotation
c. 90 rotation
d. -90 rotation

Answer 1

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

1. Original Point \( P(-1, 2) \):

   • \( x = -1 \)
   • \( y = 2 \)

2. New Point \( P'(2, 1) \):

   • \( x' = 2 \)
   • \( y' = 1 \)

Calculation of Rotation:

We can use the following transformation formulas to investigate the effect of various rotations on the coordinates.

• A 90-degree rotation counterclockwise about the origin transforms \( (x, y) \) to \( (-y, x) \).
• A 90-degree rotation clockwise (or -90 degrees counterclockwise) transforms \( (x, y) \) to \( (y, -x) \).
• A 180-degree rotation transforms \( (x, y) \) to \( (-x, -y) \).
• A 270-degree rotation counterclockwise (or -90 degrees clockwise) transforms \( (x, y) \) to \( (y, -x) \).

Checking Each Option:

1. Option a: -270 degrees (equivalently 90 degrees clockwise)

   • \( (-1, 2) \to (2, 1) \) (Correct)

2. Option b: 180 degrees

   • \( (-1, 2) \to (1, -2) \) (Incorrect)

3. Option c: 90 degrees

   • \( (-1, 2) \to (-2, -1) \) (Incorrect)

4. Option d: -90 degrees

   • \( (-1, 2) \to (2, -1) \) (Incorrect)

Given the calculations, the rotation that takes point \( P(-1, 2) \) to point \( P'(2, 1) \) is a -270 degree rotation (or 90 degrees clockwise).

Conclusion:

The correct answer is: a. -270 rotation