To determine the coordinates of point $A'$ after a 180° rotation about the origin, let's go through the steps.

Steps to Solve

1. Identify the Original Coordinates of Point A: Based on the image, it appears that point $A$ is located at $(3, 5)$.

2. Apply the Rotation Transformation: For a 180° rotation about the origin, the transformation rule is: $(x, y) \rightarrow (-x, -y)$ So, we take the coordinates $(3, 5)$ and apply this transformation: $(3, 5) \rightarrow (-3, -5)$

3. Verify the Answer: The new coordinates of $A'$ after a 180° rotation about the origin would be $(-3, -5)$.

Conclusion

The correct answer is:

• $(-3, -5)$

Would you like more details on rotation transformations or have any further questions?

Here are some related questions to expand your understanding:

1. What are the rotation rules for 90° and 270° about the origin?
2. How do the coordinates change with a 180° rotation about a point other than the origin?
3. What is the effect of a 180° rotation on the orientation of a shape?
4. Can you apply a rotation transformation to points in 3D space?
5. How does rotating a point affect its distance from the origin?

Tip: For any 180° rotation, simply negate both the x- and y-coordinates of a point.