1. **State the problem:** We need to find the image of rectangle RSTU after a dilation centered at the origin with a scale factor of $\frac{1}{5}$. The original vertices are $R(-10,0)$, $S(10,0)$, $T(10,10)$, and $U(-10,10)$. 2. **Formula for dilation:** The dilation of a point $(x,y)$ centered at the origin with scale factor $k$ is given by $$ (x', y') = (kx, ky) $$ where $(x', y')$ are the coordinates of the image point. 3. **Apply the dilation to each vertex:** - For $R(-10,0)$: $$ R' = \left(\frac{1}{5} \times -10, \frac{1}{5} \times 0\right) = (-2, 0) $$ - For $S(10,0)$: $$ S' = \left(\frac{1}{5} \times 10, \frac{1}{5} \times 0\right) = (2, 0) $$ - For $T(10,10)$: $$ T' = \left(\frac{1}{5} \times 10, \frac{1}{5} \times 10\right) = (2, 2) $$ - For $U(-10,10)$: $$ U' = \left(\frac{1}{5} \times -10, \frac{1}{5} \times 10\right) = (-2, 2) $$ 4. **Result:** The image rectangle $R'S'T'U'$ has vertices at $(-2,0)$, $(2,0)$, $(2,2)$, and $(-2,2)$. This rectangle is a scaled down version of the original by a factor of $\frac{1}{5}$, centered at the origin. **Final answer:** $$ R'(-2,0), S'(2,0), T'(2,2), U'(-2,2) $$