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

To find the coordinates of the vertices after a **180° counterclockwise rotation** around the origin, you can apply the following rule to each vertex of your figure:

### Rotation Rule for 180° Counterclockwise Around the Origin:
For any point \((x, y)\), after a 180° counterclockwise rotation about the origin, the new coordinates will be:
\[
(x', y') = (-x, -y)
\]
In other words, the coordinates of each point are simply negated.

### Example:
Let’s say you have a point \( A(3, 5) \).
- After a 180° counterclockwise rotation around the origin, the new coordinates of \( A' \) would be:
  \[
  A'( -3, -5 )
  \]

This rule applies to each vertex of any shape or polygon.

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Would you like to go over an example with multiple vertices, or do you have a specific set of points in mind?

### Related Questions:
1. What is the result of a 90° counterclockwise rotation around the origin?
2. How does rotation affect the orientation of geometric figures?
3. How do you perform a 270° clockwise rotation using coordinate transformation?
4. Can you describe the transformation matrix for a 180° rotation?
5. What is the difference between a 180° rotation and a reflection about the origin?

### Tip:
When rotating a point 180°, both the direction (clockwise or counterclockwise) results in the same coordinates, since 180° covers half of the circle.

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

Discover how to find the coordinates of any point after a 180° counterclockwise rotation around the origin. This guide covers key concepts in coordinate geometry and transformations with step-by-step examples, suitable for Grades 7-9 students.

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