Question

The translation of triangle STO (72, 72), (9, 108), and (-108, -27) after a dialation is (-8, -8), (-1,-12), and (12, 3). What is the dialation?

Answer 1

The dialation is of -(1/9)

Explanation:

I will write a matrix for the triangle before dialation. It is:

`B=\begin{bmatrix}{72} & {9} & {-108} \\ {72} & {108} & {-27}\end{bmatrix}`

The matrix after the dailation is:

`A=\begin{bmatrix}{-8} & {-1} & {12} \\ {-8} & {-12} & {3}{}\end{bmatrix}`

The relationship between the matrix is:

`A=Bx`

In which x is the dilation.

So

`\begin{bmatrix}{-8} & {-1} & {12} \\ {-8} & {-12} & {3}\end{bmatrix}=\begin{bmatrix}{72} & {9} & {-108} \\ {72} & {108} & {-27}\end{bmatrix}x`

Taking two elements at the same position, i will take the first ones:

`-8=72x`

Now we find the dilation x.

`x=-(8)/(72)=-(1)/(9)`

The dialation is of -(1/9)