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The image you uploaded presents a task involving a rotation and asks to determine the coordinates of point \( A' \), given the preimage \( A(-2, -5) \) and a rotation of 180°.

To solve this:

### Rotation of 180°
When a point \( (x, y) \) is rotated 180° about the origin, the coordinates of the point change as follows:
\[
(x', y') = (-x, -y)
\]
So, applying this rule to point \( A(-2, -5) \):

\[
A' = (-(-2), -(-5)) = (2, 5)
\]

Thus, the coordinates of \( A' \) after a 180° rotation are \( A'(2, 5) \).

The correct answer is **A'(2, 5)**.

Would you like more details or have any other questions? Here are five related questions that expand on this concept:

1. How do the coordinates change under a 90° clockwise rotation?
2. How do you perform a reflection over the x-axis for any point \( (x, y) \)?
3. How do the coordinates change under a 270° counterclockwise rotation?
4. What is the formula for a 180° rotation about a point other than the origin?
5. How would the rotation change if it was about a point different from the origin?

**Tip**: Always check the direction and center of rotation when solving transformation problems.

Graph the preimage and image of each rotation. Determine the coordinates of A'. Given: A(-2, -5), with a 180° rotation.

Learn how to find the coordinates of point A' after a 180-degree rotation of A(-2, -5) around the origin. This problem involves geometric transformations and the 180-degree rotation formula, suitable for students in Grades 7-10.

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