1. **State the problem:** We have a triangle with vertices A(1,7), B(4,7), and C(3,3). We want to find the coordinates of the reflected triangle across the line $y = x$. 2. **Reflection rule across $y = x$:** When a point $(x,y)$ is reflected across the line $y = x$, the coordinates swap places. The reflected point becomes $(y,x)$. 3. **Apply the reflection to each vertex:** - For $A(1,7)$, the reflected point $A'$ is $(7,1)$. - For $B(4,7)$, the reflected point $B'$ is $(7,4)$. - For $C(3,3)$, the reflected point $C'$ is $(3,3)$ (since $x$ and $y$ are equal, it remains the same). 4. **Final answer:** The reflected triangle has vertices $A'(7,1)$, $B'(7,4)$, and $C'(3,3)$.