Answer:
[tex]\dfrac{1}{4}[/tex]
Step-by-step explanation:
Center of dilation: O(9,0).
Line AB with A(-3,-4) and B(5,-4) is dilated with the scale factor k and center of dilation at O to form line A'B' with A'(6,-1) and B'(8,-1).
Then
[tex]OB'=kOB\\ \\OA'=kOA[/tex]
Since
[tex]OB'=\sqrt{(8-9)^2+(-1-0)^2}=\sqrt{1+1}=\sqrt{2}\\ \\OB=\sqrt{(5-9)^2+(-4-0)^2}=\sqrt{16+16}=4\sqrt{2},[/tex]
then
[tex]\sqrt{2}=k\cdot 4\sqrt{2}\\ \\k=\dfrac{1}{4}[/tex]
