Determine the scale factor used in the dilation of line segment AB , centered at the origin. (1 point)
Image shows a line segment between 1, -3 and 2, -4. Then shows another line segment between 4, -12 and 8, -16
The scale factor used in the dilation of line segment AB is 3.
This can be determined by comparing the lengths of the original line segment AB (distance between points 1, -3 and 2, -4) and the dilated line segment AB' (distance between points 4, -12 and 8, -16).
The length of AB is √((2-1)^2 + (-4-(-3))^2) = √(1^2 + (-1)^2) = √2
The length of AB' is √((8-4)^2 + (-16-(-12))^2) = √(4^2 + (-4)^2) = √(16 + 16) = √32 = 4√2
Therefore, the scale factor used in the dilation is 4√2 / √2 = 4.