1. **State the problem:** We need to dilate triangle $\triangle ABC$ centered at the origin using the scale factor $n$ from part D, then compare the side lengths of the dilated triangle $\triangle A'B'C'$ with those of $\triangle DEF$. 2. **Recall the dilation formula:** A dilation centered at the origin with scale factor $n$ transforms each point $(x,y)$ to $(nx, ny)$. 3. **Apply dilation to each vertex:** If $A=(x_A,y_A)$, then $A'=(nx_A, ny_A)$, similarly for $B$ and $C$. 4. **Calculate side lengths of $\triangle A'B'C'$:** Use the distance formula between points $P=(x_1,y_1)$ and $Q=(x_2,y_2)$: $$\text{Length} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ 5. **Compare side lengths:** Since dilation scales lengths by $n$, each side length of $\triangle A'B'C'$ should be $n$ times the corresponding side length of $\triangle ABC$. 6. **Compare $\triangle A'B'C'$ with $\triangle DEF$:** If $\triangle DEF$ is congruent to $\triangle A'B'C'$, their corresponding side lengths should be equal. **Final answer:** The side lengths of $\triangle A'B'C'$ are each $n$ times the side lengths of $\triangle ABC$, and these lengths should match those of $\triangle DEF$ if the dilation scale factor $n$ was chosen correctly. Note: Without specific coordinates or values from part D, this is the general method to perform the dilation and comparison.