1. **Problem Statement:** Reflect the kite TUVW with vertices $T(6,-10)$, $U(10,-4)$, $V(6,4)$, and $W(2,-4)$ over the line $y = x$. 2. **Reflection Rule:** When reflecting a point $(a,b)$ over the line $y = x$, the image is $(b,a)$. This means we swap the $x$ and $y$ coordinates. 3. **Apply the rule to each vertex:** - $T(6,-10) \to T'(-10,6)$ - $U(10,-4) \to U'(-4,10)$ - $V(6,4) \to V'(4,6)$ - $W(2,-4) \to W'(-4,2)$ 4. **Result:** The reflected kite $T'U'V'W'$ has vertices $T'(-10,6)$, $U'(-4,10)$, $V'(4,6)$, and $W'(-4,2)$. 5. **Explanation:** Reflection over $y=x$ swaps the coordinates, effectively flipping the figure across the diagonal line where $x=y$. This preserves distances and angles, so the kite shape remains congruent but repositioned. **Final answer:** $$ T'(-10,6),\quad U'(-4,10),\quad V'(4,6),\quad W'(-4,2) $$