1. State the problem: Dilate rectangle RSTU with vertices R(-10,-10), S(10,-10), T(10,5), U(-10,5) by a scale factor of 1/5 centered at the origin. 2. Formula: For a dilation centered at the origin with scale factor $k$, each point maps by $ (x,y) \mapsto (k x, k y) $. 3. Set the scale factor: $k=\frac{1}{5}$. 4. Apply the formula to each vertex. 5. R: $R(-10,-10) \mapsto R'(-10\cdot k,-10\cdot k)=R'(-10\cdot \frac{1}{5},-10\cdot \frac{1}{5})=R'(-2,-2)$. 6. S: $S(10,-10) \mapsto S'(10\cdot k,-10\cdot k)=S'(10\cdot \frac{1}{5},-10\cdot \frac{1}{5})=S'(2,-2)$. 7. T: $T(10,5) \mapsto T'(10\cdot k,5\cdot k)=T'(10\cdot \frac{1}{5},5\cdot \frac{1}{5})=T'(2,1)$. 8. U: $U(-10,5) \mapsto U'(-10\cdot k,5\cdot k)=U'(-10\cdot \frac{1}{5},5\cdot \frac{1}{5})=U'(-2,1)$. 9. Intermediate arithmetic: $-10\cdot \frac{1}{5}=-2$, $10\cdot \frac{1}{5}=2$, $5\cdot \frac{1}{5}=1$. 10. Final answer: The image rectangle R'S'T'U' has vertices $R'(-2,-2)$, $S'(2,-2)$, $T'(2,1)$, $U'(-2,1)$. 11. Learner note: Each coordinate is multiplied by the scale factor 1/5, which shrinks the rectangle toward the origin by a factor of 5; the dilated rectangle is centered at the origin and lies inside the original.