Determine the scale factor used in the dilation of line segment AB, centered at the origin.
A (9, 9)
B (6, 6)
A (3, 3)
B (2, 2)
To find the scale factor, we can compare the distances between the points before and after the dilation.
The distance between points A and B before the dilation is:
√((9-6)^2 + (9-6)^2) = √(3^2 + 3^2) = 3√2
The distance between points A and B after the dilation is:
√((3-2)^2 + (3-2)^2) = √(1^2 + 1^2) = √2
So the scale factor can be found by dividing the distance after the dilation by the distance before the dilation:
√2 / (3√2) = 1/3
Therefore, the scale factor used in the dilation of line segment AB is 1/3.