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

Question

−270°rotation (clockwise)
90° (counter clockwise)
180° rotation (counter clockwise)
−90° rotation (clockwise)

Answer 1

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

1. First, let's think about the rotation around the origin. The point \( P(4, 2) \) is in the first quadrant.
2. The rotated point \( P'(-2, 4) \) is in the second quadrant.

Now, let's consider the transformations:

• A \( 90^\circ \) counterclockwise rotation would transform: \[ (x, y) \rightarrow (-y, x) \] Using \( P(4, 2) \): \[ (4, 2) \rightarrow (-2, 4) \quad \text{(which matches } P' \text{)} \]

Thus, the rotation from \( P(4, 2) \) to \( P'(-2, 4) \) is a \( 90^\circ \) rotation counterclockwise.

Conclusion:

90° (counter clockwise)