https://file.aiquickdraw.com/mathbot/file/1727470822087tu5chpwt.jpg

From the screenshot you shared, the question is about rotating a point \( P_0 \) by 180 degrees around a point \( R \), such that the rotation sends \( P_0 \) to a new point \( P_1 \). The question asks which image shows the correct rotation.

In a 180-degree rotation, every point on a line moves to its opposite side, and the distance from the center of rotation (here, point \( R \)) remains the same.

- If point \( P_0 \) is located at a certain distance on one side of \( R \), then after a 180-degree rotation, point \( P_1 \) will be located at the same distance but on the opposite side of \( R \).

Based on the second image being selected (Option B), this option shows \( P_1 \) positioned correctly on the opposite side of \( R \) at an equal distance from \( R \) as \( P_0 \), which is the correct visualization of a 180-degree rotation.

### Follow-up questions:
1. Can you describe how to find the center of rotation if you only know two points?
2. What would happen to the points if the rotation was 90 degrees instead of 180?
3. How does the distance from the center of rotation affect the result of the rotation?
4. What happens to angles between points and the center during a 180-degree rotation?
5. How would you determine the new coordinates after rotating a point 180 degrees about an origin?

### Tip:
Always remember that a 180-degree rotation moves a point to the opposite side of the center, along the same straight line, and the distance from the center remains unchanged.

Which image shows point P1 such that a 180-degree rotation sends P0 to P1?

Explore how a 180-degree rotation transforms a point around a fixed center in coordinate geometry. This page explains the concept with visual aids and formulas, ideal for students in Grades 6-8.

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