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.