1. **Problem Statement:** We have quadrilateral LMNO with vertices L(3, 2), M(5, 1), N(6, 2), and O(5, 4). 2. **Transformation Rule:** The transformation rule given is $(x, y) \to (x + 2, y - 7)$. This means for each point, add 2 to the x-coordinate and subtract 7 from the y-coordinate. 3. **Applying the Transformation:** - For L(3, 2): $L' = (3 + 2, 2 - 7) = (5, -5)$ - For M(5, 1): $M' = (5 + 2, 1 - 7) = (7, -6)$ - For N(6, 2): $N' = (6 + 2, 2 - 7) = (8, -5)$ - For O(5, 4): $O' = (5 + 2, 4 - 7) = (7, -3)$ 4. **Reflection in the y-axis:** Reflection in the y-axis changes $(x, y)$ to $(-x, y)$. 5. **Applying the Reflection:** - For L(3, 2): $L'' = (-3, 2)$ - For M(5, 1): $M'' = (-5, 1)$ - For N(6, 2): $N'' = (-6, 2)$ - For O(5, 4): $O'' = (-5, 4)$ **Final answers:** - Image after transformation: $L'(5, -5), M'(7, -6), N'(8, -5), O'(7, -3)$ - Image after reflection: $L''(-3, 2), M''(-5, 1), N''(-6, 2), O''(-5, 4)$