Answer:
The scale factor is [tex]-4[/tex]
Step-by-step explanation:
Lets have a look to the co-ordinates of triangle ABC and A'B'C.
The point of C=[tex](1,-1)[/tex] and B=[tex](-1,-1)[/tex]
The point of C=[tex](1,-1)[/tex] and A'=[tex](9,-1)[/tex]
By applying distance formula we can calculate the distance of line segment :[tex]\sqrt{(x1-x)^2+(y1-y)^2}[/tex]
BC =[tex]\sqrt{(1+1)^2+(0)^2}[/tex]=[tex]\sqrt{4}[/tex]=2
Similarly CA=[tex]\sqrt{64}[/tex]=8
Scale factor = K=[tex]\frac{CA'}{BC}[/tex]=[tex]\frac{8}{2}[/tex]=4
The image and its preimage lies in opposite sides of center of dilation, C=[tex](1,-1)[/tex] therefore the scale factor will be negative.
Our final answer = -4
