Question

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

90°
rotation
90 degreesrotation

−90°
rotation
negative 90 degreesrotation

−270°
rotation
negative 270 degreesrotation

180°
rotation

Answer 1

To determine the rotation needed to transform the point \( P(4, 2) \) into \( P'(-2, 4) \), we can analyze the transformation:

1. Start by considering the original point \( P(4, 2) \).
2. If we rotate \( P \) 90 degrees counterclockwise, the transformation can be described by the formula:
\[
(x, y) \to (-y, x)
\]

Applying this to the point \( P(4, 2) \):
\[
(4, 2) \to (-2, 4)
\]

3. The output is exactly \( P'(-2, 4) \).

Thus, the rotation that describes the transformation from \( P \) to \( P' \) is a **90° rotation counterclockwise**.

The correct response is:
**90° rotation**.