1. The problem states that line segment LM is rotated 180° counterclockwise about the origin to produce L'M'. 2. The rule for a 180° counterclockwise rotation about the origin is: $$(x, y) \to (-x, -y)$$ This means every point $(x, y)$ is mapped to $(-x, -y)$. 3. To verify, consider point L at $(-8, 4)$: $$(-8, 4) \to (\cancel{-8}, \cancel{4}) \to (8, -4)$$ 4. Similarly, point M at $(-8, 8)$: $$(-8, 8) \to (8, -8)$$ 5. The rotated points L' and M' are at $(8, -4)$ and $(8, -8)$ respectively, but the problem states L' and M' are at $(4, -4)$ and $(4, -8)$, which suggests a possible typo or different scale in the graph. 6. However, the rotation rule remains the same for 180° rotation about the origin: $$(x, y) \to (-x, -y)$$ This is the standard and correct transformation rule. Final answer: $$(x, y) \to (-x, -y)$$