1. **State the problem:** We have a dilation of a black polygon to a blue polygon with center of dilation at point $P$. We need to determine if the dilation is an enlargement or reduction and find the scale factor $n$. 2. **Understanding dilation:** A dilation changes the size of a figure but keeps its shape. The scale factor $n$ tells us how much the figure is enlarged or reduced. - If $n > 1$, the dilation is an enlargement. - If $0 < n < 1$, the dilation is a reduction. 3. **Finding the scale factor:** The scale factor $n$ is the ratio of the distance from the center of dilation to a point on the image (blue polygon) over the distance from the center to the corresponding point on the original figure (black polygon). 4. **Calculate distances:** Let’s denote the center of dilation as $P$, a point on the black polygon as $B$, and the corresponding point on the blue polygon as $B'$. Then, $$n = \frac{\text{distance}(P, B')}{\text{distance}(P, B)}$$ 5. **Interpretation from the description:** The blue polygon is smaller and inside the black polygon, so the scale factor $n$ must be less than 1, indicating a reduction. 6. **Final answer:** The dilation is a **reduction**. The scale factor $n$ is a positive number less than 1, representing how much smaller the blue polygon is compared to the black polygon. Since exact coordinates are not provided, the exact numeric value of $n$ cannot be calculated here, but the reasoning confirms the nature of the dilation. **Summary:** - Dilation type: Reduction - Scale factor: $0 < n < 1$ (exact value depends on coordinates)