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)
Answer choices:
A: -1/3
B: 3
C: 1/3
D: -3
The scale factor can be found by comparing the lengths of the original line segment AB and the corresponding dilated line segment A'B'.
Using the distance formula, the length of AB is:
√[(9-6)^2 + (9-6)^2] = √[(3)^2 + (3)^2] = √(18) = 3√2
The length of A'B' can be found similarly:
√[(3-2)^2 + (3-2)^2] = √[(1)^2 + (1)^2] = √(2) = √2
The scale factor is the ratio of the lengths of the dilated line segment to the original line segment.
Therefore, the scale factor is (length of A'B') / (length of AB) = (√2) / (3√2) = 1/3
Therefore, the correct answer is C: 1/3.