Solution:
1. Reflection across the line y = -x:
- To find the image of a point (x, y) after reflection across y = -x, swap the coordinates and change their signs:
- Original point: (-5, -2)
- Swap and change signs: (-(-2), -(-5)) = (2, 5)
2. The image of the point $(-5, -2)$ after reflection across the line y = -x is (2, 5).