Question

Can you help me find the scale factor and center of the dilation, you don’t need to go into too much details because I basically got it down

Answer 1

Looking at the graph, we can say that the center of dilation is at point I since this point doesn't change.

We need to find the ratio of the distances between the new and the old.

For the new side, let's choose H'(-1, 6) and I'(3, 8)

Using distance formula :

$\begin{gathered} d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ d=\sqrt[]{(3+1)^2+(8-6)^2} \\ d=\sqrt[]{20} \end{gathered}$

And for the old or original side H(-3, 5) and I(3, 8)

$\begin{gathered} d=\sqrt[]{(3+3)^2+(8-5)^2} \\ d=\sqrt[]{45} \end{gathered}$

Take the ratio between the new and the original distances :

$\begin{gathered} \frac{\sqrt[]{20}}{\sqrt[]{45}}=\frac{2\sqrt[]{5}}{3\sqrt[]{5}} \\ \Rightarrow\frac{2}{3} \end{gathered}$

ANSWER :

The scale factor is 2/3 and the center of dilation is at I(3, 8)