https://file.aiquickdraw.com/mathbot/file/1734720354357rcnf3zqd.jpg

The problem asks for the coordinates of the vertices \( J \), \( K \), and \( L \) after a 180° counterclockwise rotation around the origin. Let's solve this step by step:

### Key Property:
Under a 180° counterclockwise rotation around the origin, the coordinates \( (x, y) \) of any point transform to \( (-x, -y) \).

### Step 1: Initial Coordinates
From the graph:
- \( J = (-8, -8) \)
- \( K = (-6, -4) \)
- \( L = (-10, -10) \)

### Step 2: Apply Rotation Rule
Using the rule \( (x, y) \to (-x, -y) \):
1. \( J(-8, -8) \to (8, 8) \)
2. \( K(-6, -4) \to (6, 4) \)
3. \( L(-10, -10) \to (10, 10) \)

### Step 3: Final Coordinates
After the 180° counterclockwise rotation:
- \( J' = (8, 8) \)
- \( K' = (6, 4) \)
- \( L' = (10, 10) \)

Let me know if you'd like a deeper explanation of the rotation process or visualization.

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**Follow-up Questions:**
1. What happens to coordinates during a 90° rotation counterclockwise?
2. How do we determine the new coordinates if a point is rotated 270° counterclockwise?
3. How would a 180° clockwise rotation compare with a 180° counterclockwise rotation?
4. Can you identify the properties of rotations that ensure congruence?
5. How would this transformation differ if it were performed with respect to a point other than the origin?

**Tip:** Always visualize the rotation as turning the graph around the origin for a clear understanding of coordinate changes!

Write the coordinates of the vertices after a rotation 180° counterclockwise around the origin.

Learn how to determine new coordinates after a 180° counterclockwise rotation around the origin. This example includes the transformation of vertices J, K, and L, applying the rotation rule (x, y) → (-x, -y). Suitable for Grades 8-10.

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