A (1,-3) B(2,-4) A' (4,-12) B' (8,-16)
determine the scale factor used in the dilation of line segment AB centered at the origin
To determine the scale factor used in the dilation of line segment AB centered at the origin, we can compare the lengths of AB and A'B'.
Using the distance formula,
AB = sqrt((2-1)^2 + (-4-(-3))^2) = sqrt(1^2 + (-1)^2) = sqrt(2)
A'B' = sqrt((8-4)^2 + (-16-(-12))^2) = sqrt(4^2 + (-4)^2) = sqrt(16 + 16) = sqrt(32) = 4 * sqrt(2)
Therefore, the scale factor used in the dilation is 4.