1. The problem asks for the translation rule that maps quadrilateral DEFG to quadrilateral D'E'F'G'. 2. A translation moves every point of a figure the same distance in the same direction. 3. The given translation moves every point 8 units to the right and 7 units up. 4. The general translation rule is written as: $$(x, y) \to (x + a, y + b)$$ where $a$ is the horizontal shift and $b$ is the vertical shift. 5. Substituting the given values, we get: $$(x, y) \to (x + 8, y + 7)$$ 6. This means every point $(x, y)$ in quadrilateral DEFG moves to $(x + 8, y + 7)$ in quadrilateral D'E'F'G'. 7. Therefore, the translation rule is: $$(x, y) \to (x + 8, y + 7)$$