1. **State the problem:** We have a quadrilateral VUST with vertices V(6,10), U(10,10), S(6,6), and T(10,6). We need to dilate this quadrilateral by a scale factor of $\frac{1}{2}$ centered at the origin (0,0). 2. **Formula for dilation:** If a point has coordinates $(x,y)$, after dilation by scale factor $k$ centered at the origin, the new coordinates $(x',y')$ are given by: $$ x' = kx, \quad y' = ky $$ 3. **Apply the formula to each vertex:** - For $V(6,10)$: $$ V' = \left( \frac{1}{2} \times 6, \frac{1}{2} \times 10 \right) = (3, 5) $$ - For $U(10,10)$: $$ U' = \left( \frac{1}{2} \times 10, \frac{1}{2} \times 10 \right) = (5, 5) $$ - For $S(6,6)$: $$ S' = \left( \frac{1}{2} \times 6, \frac{1}{2} \times 6 \right) = (3, 3) $$ - For $T(10,6)$: $$ T' = \left( \frac{1}{2} \times 10, \frac{1}{2} \times 6 \right) = (5, 3) $$ 4. **Interpretation:** Each vertex is moved closer to the origin by half its original distance, resulting in a smaller, similar quadrilateral. **Final answer:** $$ V'(3,5), \quad U'(5,5), \quad S'(3,3), \quad T'(5,3) $$