The point P(2, −5) is rotated to become P′(−2, 5) . Describe the rotation by degree and direction.(1 point)

Question

Responses

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

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

−90°rotation (clock wise)
negative 90 degreesrotation (clock wise)

90°rotation (counter clockwise)

Answer 1

To determine the rotation that takes point \( P(2, -5) \) to point \( P'(-2, 5) \), we can analyze the changes in coordinates.

1. Starting Point: \( P(2, -5) \)
2. Ending Point: \( P'(-2, 5) \)

Now, we can visualize the movement:

• The x-coordinate changed from \( 2 \) to \( -2 \), indicating a movement of \( -4 \) in the x-direction.
• The y-coordinate changed from \( -5 \) to \( 5 \), showing a movement of \( +10 \) in the y-direction.

This overall transformation suggests a rotation around the origin.

To clarify the specific rotation:

• A 180° rotation around the origin would transform the coordinates \( (x, y) \) into \( (-x, -y) \). Therefore, a point at \( (2, -5) \) would rotate to \( (-2, 5) \).
• The changes in both coordinates correspond exactly with what we see in the transformation from \( P \) to \( P' \), hence this confirms it is indeed a 180° rotation.

Thus, the correct description of the rotation is 180° rotation (counterclockwise) or 180 degrees rotation (counterclockwise). Both forms of the answer mean the same thing in this context.

Final answer: 180° rotation (counterclockwise) or 180 degrees rotation (counterclockwise).