https://file.aiquickdraw.com/mathbot/file/1729860756214slal7usj.jpg

To solve this problem, we need to rotate the triangle \( \Delta KLM \) 180° clockwise around the origin.

For a 180° clockwise rotation about the origin, the coordinates of any point \( (x, y) \) will transform into \( (-x, -y) \).

Here are the steps:
1. First, find the coordinates of points \( K \), \( L \), and \( M \) from the graph:
   - \( K = (-7, -8) \)
   - \( L = (2, -8) \)
   - \( M = (-1, -5) \)

2. Apply the 180° rotation rule \( (x, y) \rightarrow (-x, -y) \):
   - \( K(-7, -8) \rightarrow (7, 8) \)
   - \( L(2, -8) \rightarrow (-2, 8) \)
   - \( M(-1, -5) \rightarrow (1, 5) \)

3. Plot the new points:
   - \( K' = (7, 8) \)
   - \( L' = (-2, 8) \)
   - \( M' = (1, 5) \)

The image of the triangle \( \Delta KLM \) after a 180° clockwise rotation is now at the new points. 

Would you like a detailed diagram or further clarifications?

Here are 5 related questions to explore further:
1. How does the transformation rule change for a 90° rotation?
2. What are the effects of a reflection over the x-axis for triangle \( \Delta KLM \)?
3. How do rotations of different angles (e.g., 270°) affect the coordinates of points?
4. What is the significance of rotating around a point other than the origin?
5. Can you describe the properties of a 180° rotation in terms of distance and orientation?

**Tip:** A 180° rotation is equivalent to reflecting the figure twice—once over the x-axis and then over the y-axis.

Graph the image of ∆KLM after a rotation 180° clockwise around the origin.

Learn how to rotate triangle ∆KLM 180° clockwise around the origin on a coordinate plane. This problem involves geometric transformations, specifically the rotation rule (x, y) → (-x, -y), and is suitable for students in Grades 8-10.

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