The point P(4, 2) is rotated to become P′(−2, 4) . Describe the rotation by degree and direction.(1 point)

Question

Responses

180°rotation (counter clockwise)
180 degreesrotation (counter clockwise)

90°rotation (counter clockwise)
90 degreesrotation (counter clockwise)

270°rotation (counter clockwise)
270 degreesrotation (counter clockwise)

−90°rotation (clock wise)

Answer 1

To determine the degree and direction of the rotation from point \( P(4, 2) \) to point \( P'(-2, 4) \), we can analyze the transformation geometrically.

1. Identify the original and new points:

   • Original point \( P(4, 2) \)
   • New point \( P'(-2, 4) \)

2. Visualize the rotation:

   • A 90° rotation counterclockwise around the origin transforms the point \( (x, y) \) to \( (-y, x) \).
   • Applying this rule: \( P(4, 2) \) becomes \( P''(-2, 4) \).

3. Result:

   • Since the transformation matches, we conclude that the rotation from \( P \) to \( P' \) is a 90° rotation counterclockwise.

Therefore, the correct response is:

90° rotation (counter clockwise).