1. **State the problem:** We need to find the image of triangle $\triangle JKL$ under a dilation centered at the origin with scale factor $\frac{1}{3}$. 2. **Recall the dilation formula:** For a point $(x,y)$, the image after dilation centered at the origin with scale factor $k$ is given by: $$ (x', y') = (kx, ky) $$ 3. **Apply the scale factor $\frac{1}{3}$ to each vertex:** - For $J(2, -3)$: $$ J' = \left(\frac{1}{3} \times 2, \frac{1}{3} \times (-3)\right) = \left(\frac{2}{3}, -1\right) $$ - For $K(5, -6)$: $$ K' = \left(\frac{1}{3} \times 5, \frac{1}{3} \times (-6)\right) = \left(\frac{5}{3}, -2\right) $$ - For $L(4, -8)$: $$ L' = \left(\frac{1}{3} \times 4, \frac{1}{3} \times (-8)\right) = \left(\frac{4}{3}, -\frac{8}{3}\right) $$ 4. **Interpretation:** Each coordinate of the original triangle is multiplied by $\frac{1}{3}$, shrinking the triangle towards the origin by a factor of 3. 5. **Final answer:** The image of $\triangle JKL$ under the dilation is the triangle with vertices: $$ J'\left(\frac{2}{3}, -1\right), K'\left(\frac{5}{3}, -2\right), L'\left(\frac{4}{3}, -\frac{8}{3}\right) $$