What is the scale factor of a single dilation between the preimage ABC and image A'B'C'?

Hi! To find the scale factor of the dilation between the preimage ABC and image A'B'C', we can compare the corresponding lengths of the sides.

Using the distance formula, we can find the lengths of the sides:

AB = √((3-2)^2 + (2-1)^2) = √2
A'B' = √((9-6)^2 + (6-3)^2) = √18 = 3√2

BC = √((1-3)^2 + (3-2)^2) = √5
B'C' = √((3-9)^2 + (9-6)^2) = √99 ≈ 3√11

AC = √((1-2)^2 + (3-1)^2) = √5
A'C' = √((3-6)^2 + (9-3)^2) = √72 = 6√2

By comparing the sides, we can see that the scale factor is 3√2.

Hope this helps! Is there anything else you need?