Question

Find the scale factor of the dilation. answer options are 2 3 4 8

Answer 1

We need to compare the distances between the vertices of the original and the dilated image.

The original image is triangle JHG, solve for the distance between the points J(2, 2) and G(-2, -2)

Using the distance formula :

`d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}`
`\begin{gathered} d_(jg)=\sqrt[]{(-2-2)^2+(-2-2)^2} \\ =\sqrt[]{16+16} \\ =\sqrt[]{32} \\ =4\sqrt[]{2} \end{gathered}`

Next is to get the distance between the points of the dilated image, A(4, 4) and C(-4, -4)

`\begin{gathered} d_(ab)=\sqrt[]{(-4-4)^2+(-4-4)^2} \\ =\sqrt[]{64+64} \\ =\sqrt[]{128} \\ =8\sqrt[]{2} \end{gathered}`

Comparing the two distances :

`8\sqrt[]{2}\quad \text{ is twice of}\quad 4\sqrt[]{2}`

Therefore, the scale factor is 2

ANSWER :

2