Question

In the diagram, the circle will be dilated by a scale factor of 3 about the origin. The points C, A, and B map to C', A', and B' after the dilation. What is the length of C' B' ? Use the distance formula to help you decide.

Answer 1

The distance between the two points has a linear relationship with the lengths of the segments. So if we dilate the circle with a scale factor of 3, the distance between the two would also be dilated with a scale factor of 3. Therefore let us first find for the distance or length of CB. The distance formula is:

d^2 = (x2 – x1)^2 + (y2 – y1)^2

where:

C = (x1, y1) = (8, 10)

B = (x2, y2) = (12, 13)

Therefore the length of CB is:

d^2 = (12 – 8)^2 + (13 – 10)^2

d^2 = 25

d = 5

Therefore the length of C’B’ is 3 times of this since dilation means expansion:

C’B’ = 5 * 3 = 15