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.