https://r2.erweima.ai/mathbot/image/1725643086726t4wam255.jpg

The problem in the image asks to graph the image of point \( M(-6, -10) \) after a 180° clockwise rotation around the origin.

### Step-by-Step Solution:

1. **Rotation Rule for 180° Clockwise**:
   A 180° clockwise rotation (which is the same as a 180° counterclockwise rotation) about the origin transforms a point \((x, y)\) into \((-x, -y)\).

2. **Apply the Rule**:
   The original point is \( M(-6, -10) \).
   - After a 180° rotation, the new coordinates of \( M' \) will be:
   \[
   M' = (-(-6), -(-10)) = (6, 10)
   \]

3. **Plotting the Point**:
   The point \( M'(6, 10) \) can now be plotted on the graph.

Would you like a more detailed explanation or any further clarifications? Here are some related questions to explore:

1. What is the general formula for a rotation of 90° clockwise?
2. How does a 270° clockwise rotation differ from a 180° rotation?
3. How do we calculate the coordinates of a point after any arbitrary rotation?
4. Can you describe the geometric properties that remain unchanged after rotation?
5. How can we distinguish between a reflection and a rotation based on coordinates?

**Tip**: When rotating points around the origin, always apply the appropriate transformation rule based on the degree of rotation.

Graph the image of M(-6, -10) after a rotation 180° clockwise around the origin.

Learn how to graph the image of point M(-6, -10) after a 180° clockwise rotation around the origin. This guide covers key concepts in coordinate geometry, including the rotation rule and theorems, suitable for students in Grades 8-10.

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