Listen REASONING Your friend prints a 4 -inch by 6 -inch photo for you from the school dance. All you have is an 8 -inch by 10 -inch frame. Can you dilate the photo to fit the frame? The scale factor for the shorter sides is and the scale factor for the longer sides is yes no : \( : \frac{1}{2} \) : 2 : \( \frac{5}{2} \) : \( \frac{5}{3} \) 1 :: \( \frac{4}{5} \) : \( \frac{5}{4} \) :: \( \frac{3}{5} \) \( :: \frac{2}{3} \) : \( \frac{4}{3} \) :: \( \frac{3}{4} \) Previous 1 2 3 4 5 6 7 Next

Yes, you can dilate the photo to fit the 8-inch by 10-inch frame. To do this, you need to determine the appropriate scale factors for both the shorter and longer sides of the photo. ### Calculating the Scale Factors 1. **Shorter Side (4 inches to 8 inches):** \[ \text{Scale Factor} = \frac{\text{Frame Shorter Side}}{\text{Photo Shorter Side}} = \frac{8}{4} = 2 \] So, the scale factor for the shorter side is **2**. 2. **Longer Side (6 inches to 10 inches):** \[ \text{Scale Factor} = \frac{\text{Frame Longer Side}}{\text{Photo Longer Side}} = \frac{10}{6} = \frac{5}{3} \] So, the scale factor for the longer side is **\(\frac{5}{3}\)**. ### Summary - **Scale Factor for Shorter Side:** \(2\) - **Scale Factor for Longer Side:** \(\frac{5}{3}\) By applying these scale factors, you can effectively enlarge your 4-inch by 6-inch photo to fit perfectly within an 8-inch by 10-inch frame.