Question

Find the scale factor that△XYZ△XYZ was dilated by to get △ABC△ABC if centered at point (-4, 0). The coordinates are A(0, -4), B(6, 6), C(8, -4), X(-2, -2), Y(1, 3) and Z(2, -2).

Answer 1

Remember that

The dilation is a non rigid transformation that produces similar figures

If two figures are similar, then the ratio of its corresponding sides is proportional, and this ratio is called the scale factor

In this problem

triangle XYZ and triangle ABC are similar

that means

XY/AB=YZ/BC=XZ/AC=scale factor

step 1

Find distance XY

Apply formula to calculate the distance between two points

X(-2, -2), Y(1, 3)

`\begin{gathered} XY=\sqrt[]{(3+2)^2+(1+2)^2} \\ XY=\sqrt[]{34} \end{gathered}`

step 2

Find the distance AB

Apply formula to calculate the distance between two points

A(0, -4), B(6, 6)

`\begin{gathered} AB=\sqrt[]{(6+4)^2+(6-0)^2} \\ AB=\sqrt[\square]{136} \end{gathered}`

step 3

Find the scale factor

scale factor=AB/XY

`\text{scale factor=}\frac{\sqrt[]{136}}{\sqrt[\square]{34}}=2`

the scale factor is 2