A (-3, 4) to B (2, -4) and A' (-6, 8) to B' (4,-8).
Determine the scale factor used in the dilation of line AB, with a center point of dilation at the origin.
The scale factor of a dilation can be determined by comparing the lengths of the corresponding line segments before and after the dilation.
The length of the line segment AB can be found using the distance formula:
AB = sqrt((2 - (-3))^2 + (-4 - 4)^2) = sqrt(5^2 + (-8)^2) = sqrt(25 + 64) = sqrt(89)
The length of the line segment A'B' can be found using the distance formula:
A'B' = sqrt((4 - (-6))^2 + (-8 - 8)^2) = sqrt(10^2 + (-16)^2) = sqrt(100 + 256) = sqrt(356)
To find the scale factor, we divide the length of A'B' by the length of AB:
Scale factor = A'B' / AB = sqrt(356) / sqrt(89)
Simplifying the expression:
Scale factor = sqrt(356) / sqrt(89) = sqrt(356/89) = sqrt(4) = 2
Therefore, the scale factor used in the dilation of line AB is 2.