1. **State the problem:** We need to find the image of square JKLM after a dilation centered at the origin with a scale factor of $\frac{1}{5}$. The original vertices are $J(-5,0)$, $K(5,0)$, $L(5,10)$, and $M(-5,10)$. 2. **Formula for dilation:** The dilation of a point $(x,y)$ centered at the origin with scale factor $k$ is given by $$ (x', y') = (kx, ky) $$ 3. **Apply the dilation to each vertex:** - For $J(-5,0)$: $$ J' = \left(\frac{1}{5} \times -5, \frac{1}{5} \times 0\right) = (-1, 0) $$ - For $K(5,0)$: $$ K' = \left(\frac{1}{5} \times 5, \frac{1}{5} \times 0\right) = (1, 0) $$ - For $L(5,10)$: $$ L' = \left(\frac{1}{5} \times 5, \frac{1}{5} \times 10\right) = (1, 2) $$ - For $M(-5,10)$: $$ M' = \left(\frac{1}{5} \times -5, \frac{1}{5} \times 10\right) = (-1, 2) $$ 4. **Conclusion:** The image of square JKLM after dilation with scale factor $\frac{1}{5}$ centered at the origin has vertices $J'(-1,0)$, $K'(1,0)$, $L'(1,2)$, and $M'(-1,2)$.