Answer:
The dialation is of -(1/9)
Step-by-step explanation:
I will write a matrix for the triangle before dialation. It is:
[tex]B=\begin{bmatrix}{72} & {9} & {-108} \\ {72} & {108} & {-27}\end{bmatrix}[/tex]The matrix after the dailation is:
[tex]A=\begin{bmatrix}{-8} & {-1} & {12} \\ {-8} & {-12} & {3}{}\end{bmatrix}[/tex]The relationship between the matrix is:
[tex]A=Bx[/tex]In which x is the dilation.
So
[tex]\begin{bmatrix}{-8} & {-1} & {12} \\ {-8} & {-12} & {3}\end{bmatrix}=\begin{bmatrix}{72} & {9} & {-108} \\ {72} & {108} & {-27}\end{bmatrix}x[/tex]Taking two elements at the same position, i will take the first ones:
[tex]-8=72x[/tex]Now we find the dilation x.
[tex]x=-\frac{8}{72}=-\frac{1}{9}[/tex]The dialation is of -(1/9)
