Question

the polygon ABCDE is dilated using the origin at the center of dilation form polygon a b c d e determine the scale factor used to create this transformation

Answer 1

When we are working with dilations, we have as a regular rule the following:

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

where k is the scale factor. Now, in this case, we have that A=(-4,2) and A'=(-2,1), therefore:

`\begin{gathered} D_k(-4,2)=(-4k,2k)=(-2,1) \\ \Rightarrow-4k=-2\text{ and} \\ 2k=1 \\ \Rightarrow k=(-2)/(-4)=(1)/(2) \\ \text{and} \\ k=(1)/(2) \end{gathered}`

therefore, the scale factor is k=1/2