The scale factor can be determined by comparing the length of the original line segment AB to the length of the dilated line segment AB.
Original line segment AB:
AB = sqrt((2-1)^2 + (-4-(-3))^2)
AB = sqrt(1^2 + 1^2)
AB = sqrt(2)
Dilated line segment AB:
AB' = sqrt((8-4)^2 + (-16-(-12))^2)
AB' = sqrt(4^2 + 4^2)
AB' = sqrt(32)
Scale Factor:
Scale factor = AB'/AB
Scale factor = sqrt(32)/sqrt(2)
Scale factor ≈ 2.83
Therefore, the scale factor used in the dilation of line segment AB centered at the origin is approximately 2.83.