1. **State the problem:** We need to graph and label the image of quadrilateral ABCD after a translation 4 units left and 3 units down. 2. **Given vertices:** - A(4,4) - B(6,4) - C(5,2) - D(4,1) 3. **Translation formula:** For a translation by $h$ units horizontally and $k$ units vertically, the new coordinates $(x', y')$ are given by: $$ x' = x + h $$ $$ y' = y + k $$ 4. **Apply translation:** Here, $h = -4$ (4 units left) and $k = -3$ (3 units down). Calculate each vertex: - $A': (4 - 4, 4 - 3) = (0, 1)$ - $B': (6 - 4, 4 - 3) = (2, 1)$ - $C': (5 - 4, 2 - 3) = (1, -1)$ - $D': (4 - 4, 1 - 3) = (0, -2)$ 5. **Result:** The translated quadrilateral has vertices $A'(0,1)$, $B'(2,1)$, $C'(1,-1)$, and $D'(0,-2)$. 6. **Explanation:** Translation moves every point of the figure the same distance in the same direction without changing its shape or size.