1. **Problem:** Find the image coordinates after translation. (a) Given point $(-2,4)$ and translation vector $(-3,2)$. Formula for translation: $$ (x,y) \to (x + a, y + b) $$ where $(a,b)$ is the translation vector. Step 1: Apply translation to $(-2,4)$: $$ (-2,4) \to (-2 + (-3), 4 + 2) = (-2 - 3, 6) = (-5,6) $$ (b) Given point $(0,2)$ and translation vector $(3,1)$. Step 2: Apply translation to $(0,2)$: $$ (0,2) \to (0 + 3, 2 + 1) = (3,3) $$ **Final answers:** (a) $(-5,6)$ (b) $(3,3)$