1. **Problem Statement:** Reflect the polygon ABCD with vertices A(2, -2), B(-2, 2), C(0, 4), and D(4, 0) across the line $y = x$. 2. **Reflection Formula:** 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) reflects to A'(-2, 2) - B(-2, 2) reflects to B'(2, -2) - C(0, 4) reflects to C'(4, 0) - D(4, 0) reflects to D'(0, 4) 4. **Explanation:** Reflection across $y = x$ swaps the $x$ and $y$ coordinates of each point. This is why the reflected polygon's vertices are the original vertices with their coordinates reversed. 5. **Final reflected points:** $$A'(-2, 2), B'(2, -2), C'(4, 0), D'(0, 4)$$