https://file.aiquickdraw.com/mathbot/file/1725516822619rax72djm.jpg

The image shows a geometric figure on a coordinate plane that has been rotated. The task is to identify the degrees of rotation.

Let's analyze the problem:

1. The original figure (pre-image) is labeled \( P, Q, R, S \).
2. The rotated figure (image) is labeled \( P', Q', R', S' \).

Since the figures are on a coordinate grid, we can deduce the rotation by observing the change in the positions of the points relative to the origin. 

### Steps to Identify the Rotation:
1. **Identify Corresponding Points**: Find the coordinates of a point and its rotated image.
2. **Determine the Rotation**: By comparing the coordinates of these points, we can determine how the figure has been rotated around the origin.

### Example:
- Let's assume \( P(x_1, y_1) \) rotates to \( P'(x_2, y_2) \).
- A 90° clockwise rotation would change \( (x_1, y_1) \) to \( (y_1, -x_1) \).
- A 180° rotation would change \( (x_1, y_1) \) to \( (-x_1, -y_1) \).
- A 270° clockwise rotation (or 90° counterclockwise) would change \( (x_1, y_1) \) to \( (-y_1, x_1) \).

From the image, the transformation suggests a **180° rotation** because each point has been moved to the exact opposite quadrant without changing the relative distances from the origin.

### Conclusion:
The degree of rotation for the figure is **180°**.

Would you like more details or have any questions about this rotation? Here are some related questions for further exploration:

1. What happens to the coordinates of a point after a 90° rotation clockwise?
2. How would the coordinates change after a 270° rotation counterclockwise?
3. What are the effects of reflecting a figure over the x-axis or y-axis?
4. How can we determine the center of rotation if it's not at the origin?
5. How do rotational transformations differ from other rigid motions like translations?

**Tip:** To verify rotations, always compare the coordinates of corresponding points in the pre-image and image!

Identify the degrees of rotation for the given geometric figure.

Learn how to identify the degrees of rotation for a given geometric figure on a coordinate plane. This problem covers key concepts in geometry, including rotational symmetry and coordinate transformations. Suitable for students in Grades 7-9.

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