Question

The blue shape is a dilation of the black shape. The scale factor is ____. Simplify your answer and write it as a proper fraction, improper fraction, or a whole number.

Answer 1

We have tjhe general rule for dilations:

$D_k(x,y)=(kx,ky)$

where k is the scale factor.

In this case, we can take the points (10,0) and the dilated point (8,0) to find the scale factor like this:

$\begin{gathered} D_k(10,0)=(10k,0k)=(8,0) \\ \Rightarrow10k=8 \\ \Rightarrow k=\frac{8}{10}=\frac{4}{5} \\ k\text{=}\frac{4}{5} \end{gathered}$

therefore, the scale factor is k=4/5