Determine the scale factor used in the dilation of line AB , with a center point of dilation at the origin.
A (-3, 4) B (2, -4) A' (-6, 8) B' (4, -8)
The scale factor used in the dilation of line AB is 2. This can be determined by calculating the distance between points A and B and then calculating the distance between points A' and B'.
Distance between A and B:
AB = sqrt((2 - (-3))^2 + (-4 - 4)^2)
AB = sqrt(5^2 + 8^2)
AB = sqrt(25 + 64)
AB = sqrt(89)
Distance between A' and B':
A'B' = sqrt((4 - (-6))^2 + (-8 - 8)^2)
A'B' = sqrt(10^2 + (-16)^2)
A'B' = sqrt(100 + 256)
A'B' = sqrt(356)
To calculate the scale factor, we can divide the distance between A' and B' by the distance between A and B:
Scale factor = A'B' / AB
Scale factor = sqrt(356) / sqrt(89)
Scale factor = sqrt(4)
Scale factor = 2
Therefore, the scale factor used in the dilation of line AB is 2.