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.