Question

ABC:
A = (2, 1)
B = (3, 2)
C = (1, 3)

A'B'C':
A' = (6, 3)
B' = (9, 6)
C' = (3, 9)

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

Answer 1

To find the scale factor of a dilation, we can compare the distances between corresponding points in the preimage and image.

In this case, let's compare the distance between A and B in the preimage to the distance between A' and B' in the image.

Distance between A and B:
sqrt((3 - 2)^2 + (2 - 1)^2) = sqrt(1 + 1) = sqrt(2)

Distance between A' and B':
sqrt((9 - 6)^2 + (6 - 3)^2) = sqrt(3^2 + 3^2) = sqrt(18) = 3sqrt(2)

The scale factor is the ratio of the length of the corresponding segments, so the scale factor is:

(3sqrt(2)) / sqrt(2) = 3

Therefore, the scale factor of the dilation between the preimage ABC and image A'B'C' is 3.