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You provided an image that asks for the coordinates of the vertices after a 180° counterclockwise rotation around the origin. Here's how we can solve this step by step.

### Current coordinates of the vertices:
Looking at the grid, the original coordinates are:
- \( M (3, 4) \)
- \( L (7, 4) \)
- \( J (3, 0) \)
- \( K (7, 0) \)

### Rule for a 180° counterclockwise rotation:
For a 180° rotation around the origin, the rule is:
\[
(x, y) \rightarrow (-x, -y)
\]
This means we change the sign of both the x and y coordinates.

### Applying the rule:
1. For \( M (3, 4) \), applying the rule:
   \[
   M' (-3, -4)
   \]
2. For \( L (7, 4) \), applying the rule:
   \[
   L' (-7, -4)
   \]
3. For \( J (3, 0) \), applying the rule:
   \[
   J' (-3, 0)
   \]
4. For \( K (7, 0) \), applying the rule:
   \[
   K' (-7, 0)
   \]

### Final coordinates after the 180° rotation:
- \( M' (-3, -4) \)
- \( L' (-7, -4) \)
- \( J' (-3, 0) \)
- \( K' (-7, 0) \)

Would you like a deeper explanation or have any other questions? Here are some related questions for further practice:

1. What is the rule for a 90° clockwise rotation around the origin?
2. How would the coordinates change for a 270° counterclockwise rotation?
3. What would happen to the shape if it were reflected across the x-axis instead of rotated?
4. How does the area of the figure change after a rotation or reflection?
5. What are the coordinates after a 360° rotation, and why?

**Tip:** When performing rotations, make sure to apply the rules consistently to all points, and check how the figure moves in relation to the origin.

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

Learn how to find the new coordinates after rotating a figure 180° counterclockwise around the origin. This solution covers the application of the rotation formula on the coordinate plane. Suitable for Grade 8-10 students.

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