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=(8)/(10)=(4)/(5) \\ k\text{=}(4)/(5) \end{gathered}`

therefore, the scale factor is k=4/5