determine the scale factor used in the dilation of line AB with a centered point of dilation at the origin A:(9, 9) B: (6, 6) A: (3, 3) B: (2, 2)
A. -3
B. - 1/3
C. 3
D. 1/3
To find the scale factor, we can use the formula:
scale factor = distance of image / distance of pre-image
The distance between points A and B in the pre-image is:
AB = sqrt((9 - 6)^2 + (9 - 6)^2) = sqrt(3^2 + 3^2) = sqrt(18) = 3√2
The distance between points A and B in the image is:
AB' = sqrt((3 - 2)^2 + (3 - 2)^2) = sqrt(1^2 + 1^2) = sqrt(2)
Therefore, the scale factor is:
scale factor = AB' / AB = sqrt(2) / 3√2 = 1/3
Thus, the answer is D. 1/3.