1. **Problem Statement:** We have two polygons, one on the left with vertices including $M$ and $N$, and a smaller scaled copy on the right with vertices including $I$, $H$, $F$, and $G$. We need to find which side on the right corresponds to segment $MN$ on the left and determine the scale factor. 2. **Identifying Corresponding Sides:** Since the right figure is a scaled copy of the left, each vertex corresponds to a vertex on the other figure. Given the order and labels, segment $MN$ on the left corresponds to segment $HG$ on the right because $M$ corresponds to $H$ and $N$ corresponds to $G$. 3. **Finding the Scale Factor:** The scale factor is the ratio of the length of a side on the right figure to the corresponding side on the left figure. 4. **Calculate Length of $MN$:** Suppose the coordinates of $M$ and $N$ are known or can be read from the grid. For example, if $M=(x_1,y_1)$ and $N=(x_2,y_2)$, then $$\text{Length}(MN) = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ 5. **Calculate Length of $HG$:** Similarly, if $H=(x_3,y_3)$ and $G=(x_4,y_4)$, $$\text{Length}(HG) = \sqrt{(x_4 - x_3)^2 + (y_4 - y_3)^2}$$ 6. **Compute Scale Factor:** $$\text{Scale Factor} = \frac{\text{Length}(HG)}{\text{Length}(MN)}$$ 7. **Interpretation:** The scale factor tells us how much smaller or larger the right figure is compared to the left. If the scale factor is less than 1, the right figure is smaller. **Final answers:** - The side on the right corresponding to segment $MN$ is segment $HG$. - The scale factor is the ratio of lengths $\frac{HG}{MN}$ calculated from their coordinates.