1. **Problem Statement:** Quadrilateral ABCD is dilated to form quadrilateral EFGH. We are given side lengths of ABCD as 8 (CB) and 10 (BA), and corresponding side lengths of EFGH as 3.2 (EF) and 6 (HG). We need to find the scale factor of the dilation. 2. **Formula and Concept:** The scale factor $k$ in a dilation relates the lengths of corresponding sides by the formula: $$k = \frac{\text{length of image side}}{\text{length of original side}}$$ 3. **Calculate scale factor using side CB and EF:** $$k = \frac{3.2}{8} = 0.4$$ 4. **Calculate scale factor using side BA and HG:** $$k = \frac{6}{10} = 0.6$$ 5. **Check for consistency:** The scale factor should be the same for all corresponding sides in a dilation. Here, the two calculations give different values (0.4 and 0.6), which suggests either a mistake in labeling or the quadrilaterals are not similar by dilation. 6. **Assuming the problem expects the scale factor from the given pairs, the correct scale factor is the ratio of corresponding sides. Since the problem states dilation, we take the consistent pair. The sides 8 and 3.2 correspond, so the scale factor is $0.4$. **Final answer:** The scale factor used for the dilation is $0.4$.