Question

Determine the scale factor used in the dilation of line segment AB, centered at the origin.

A (1, -3)
B (2, -4)

A (4, -12)
B (8, -16)

Answer 1

To find the scale factor, we can compare the distance between the two points before and after the dilation.

Before dilation:
The distance between A and B is sqrt((2-1)^2+(-4-(-3))^2) = sqrt(1+1) = sqrt(2).

After dilation:
The distance between A and B is sqrt((8-4)^2+(-16-(-12))^2) = sqrt(16+16) = sqrt(32).

Therefore, the scale factor is the ratio of the distance after dilation to the distance before dilation:
sqrt(32)/sqrt(2) = sqrt(32/2) = sqrt(16) = 4.

So the scale factor is 4.