Determine the scale factor used in the dilation of line AB, with a center point of dilation at the origin. A' (-6,8) B' (4,-8) and A (-3,4) B (2,-4)
To determine the scale factor used in the dilation of line AB, we can compare the lengths of AB and A'B'.
The length of AB can be calculated 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 A'B' can be calculated using the distance formula as well:
A'B' = sqrt((4 - (-6))^2 + (-8 - 8)^2)
= sqrt(10^2 + (-16)^2)
= sqrt(100 + 256)
= sqrt(356)
The scale factor can be calculated as the ratio of the lengths of A'B' and AB:
Scale factor = A'B' / AB
= sqrt(356) / sqrt(89)
≈ 1.884
Therefore, the scale factor used in the dilation is approximately 1.884.