1. **Problem Statement:** We are given two figures and asked to graph and label their images after applying two transformations: - Reflection across the line $y = x$ for the quadrilateral with vertices $K, L, S, X$. - Reflection across the $x$-axis for the triangle with vertices $Z, X, D$. 2. **Reflection Across the Line $y = x$:** - The rule for reflecting a point $(a,b)$ across the line $y = x$ is to swap the coordinates. - So, the image of $(a,b)$ is $(b,a)$. 3. **Reflection Across the $x$-Axis:** - The rule for reflecting a point $(a,b)$ across the $x$-axis is to keep the $x$-coordinate the same and negate the $y$-coordinate. - So, the image of $(a,b)$ is $(a,-b)$. 4. **Applying Reflection Across $y = x$ to Quadrilateral $K, L, S, X$:** - If $K = (x_1,y_1)$, then $K' = (y_1,x_1)$. - Similarly for $L, S, X$. 5. **Applying Reflection Across $x$-Axis to Triangle $Z, X, D$:** - If $Z = (x_2,y_2)$, then $Z' = (x_2,-y_2)$. - Similarly for $X, D$. 6. **Summary:** - Reflection across $y = x$: $(a,b) \to (b,a)$. - Reflection across $x$-axis: $(a,b) \to (a,-b)$. Since the exact coordinates are not provided, the transformations are described generally. **Final answer:** - The image of each vertex of the quadrilateral after reflection across $y = x$ is obtained by swapping its coordinates. - The image of each vertex of the triangle after reflection across the $x$-axis is obtained by negating the $y$-coordinate.