Answer:
[tex]\text{Scale factor}=\frac{5}{8}[/tex]
Step-by-step explanation:
We have been given an image of two pentagons and we are asked to find the scale factor of dilation.
Since the corresponding sides of pre-image are proportional to the corresponding sides of image after dilation, so we can find the scale fctor for the given dilation as:
[tex]\text{Pre-image}\times \text{Scale factor}=\text{ Image after dilation}[/tex]
Upon substituting the given lengths of corresponding sides we will get,
[tex]16 \times \text{Scale factor}=10[/tex]
Dividing both sides by 16 we will get,
[tex]\frac{16 \times \text{Scale factor}}{16}=\frac{10}{16}[/tex]
[tex]\text{Scale factor}=\frac{2*5}{2*8}[/tex]
[tex]\text{Scale factor}=\frac{5}{8}[/tex]
Therefore, the scale factor of given dilation is [tex]\frac{5}{8}[/tex].
