1. **State the problem:** We need to find a series of transformations that map polygon ABCDE with vertices near (1,3), (1,2), (2,1), (3,1), (3,3) onto polygon A'B'C'D'E' with vertices near (-6,-5), (-7,-3), (-9,-5), (-9,-7), (-7,-8). 2. **Identify the transformations:** We observe that ABCDE is in the first quadrant and A'B'C'D'E' is in the third quadrant, larger and reflected. 3. **Step 1: Translation to origin (optional for clarity):** Translate ABCDE so that vertex A at (1,3) moves to the origin by subtracting (1,3) from all points. 4. **Step 2: Reflection about the origin:** Reflect the polygon about the origin, which maps $(x,y)$ to $(-x,-y)$. 5. **Step 3: Dilation (scaling):** Calculate scale factor by comparing distances. For example, distance from A to B in ABCDE is approximately $\sqrt{(1-1)^2+(3-2)^2}=1$. Distance from A' to B' in A'B'C'D'E' is approximately $\sqrt{(-6+7)^2+(-5+3)^2}=\sqrt{1^2+2^2}=\sqrt{5}$. Scale factor $k=\sqrt{5}$. 6. **Step 4: Translation to final position:** Translate the reflected and scaled polygon so that the origin maps to A' at $(-6,-5)$. 7. **Summary of transformations:** - Translate by $(-1,-3)$ to move A to origin. - Reflect about origin: $(x,y) \to (-x,-y)$. - Dilate by factor $k=\sqrt{5}$. - Translate by $(-6,-5)$ to move origin to A'. This series maps ABCDE onto A'B'C'D'E'.