1. **State the problem:** We need to reflect the polygon ABCD with vertices A(2, -2), B(4, -2), C(4, -4), and D(2, -4) across the line $y = x$. 2. **Formula for reflection across $y = x$:** When reflecting a point $(x, y)$ across the line $y = x$, the coordinates swap places. The reflected point is $(y, x)$. 3. **Apply the formula to each vertex:** - $A(2, -2) \to A'(-2, 2)$ - $B(4, -2) \to B'(-2, 4)$ - $C(4, -4) \to C'(-4, 4)$ - $D(2, -4) \to D'(-4, 2)$ 4. **Result:** The reflected polygon A'B'C'D' has vertices at $A'(-2, 2)$, $B'(-2, 4)$, $C'(-4, 4)$, and $D'(-4, 2)$. This completes the reflection across the line $y = x$.