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!