The point P (4,2) is rotate to become P'(-2,4). Describe the rotation by degree and direction.(1 point)

Question

Responses

90°rotation
90 degreesrotation

−90°rotation
negative 90 degreesrotation

−270°rotation
negative 270 degreesrotation

180°rotation

Answer 1

To determine the rotation that takes point \( P(4, 2) \) to point \( P'(-2, 4) \), we can analyze the transformation.

1. Visualize the Points:

   • Point \( P(4, 2) \) is located in the first quadrant.
   • Point \( P'(-2, 4) \) is located in the second quadrant.

2. Calculate the Angle of Rotation:

   • Estimate the angle of rotation from point \( P \) to point \( P' \).

   Using coordinates:

   • To rotate a point \( (x, y) \) counterclockwise by 90 degrees, the new coordinates will be \( (-y, x) \).
   • For a 90 degrees push of rotation:
     • \( (4, 2) \) would transform to \( (-2, 4) \), which matches \( P'(-2, 4) \).

   Therefore, \( P \) has been rotated counterclockwise by 90 degrees to reach \( P' \).

3. Conclusion:

Based on the transformation, the answer is:

• 90° rotation (counterclockwise).

So the response is: 90° rotation.