1. **State the problem:** We need to find the image of trapezoid DEFG after translating it 8 units left and 11 units down. 2. **Recall the translation formula:** For a point $(x,y)$, translating $a$ units left and $b$ units down results in the point $(x - a, y - b)$. 3. **Apply the translation to each vertex:** - $D(4,1) \to D'(4 - 8, 1 - 11) = (-4, -10)$ - $E(8,1) \to E'(8 - 8, 1 - 11) = (0, -10)$ - $F(4,9) \to F'(4 - 8, 9 - 11) = (-4, -2)$ - $G(-2,9) \to G'(-2 - 8, 9 - 11) = (-10, -2)$ 4. **Conclusion:** The translated trapezoid has vertices $D'(-4,-10)$, $E'(0,-10)$, $F'(-4,-2)$, and $G'(-10,-2)$. This matches the given image coordinates after translation.