A(9,9) B(6,6) A'(3,3) B'(2,2)
determine the scale factor used in the dilation of line AB, with a center point of dilation at the origin.
a 3
b -1/3
c 1/3
d -3
To determine the scale factor used in the dilation of line AB, we can compare the distances between the points before and after dilation.
Let's calculate the distance between points A and B:
AB = √((6-9)^2 + (6-9)^2)
= √((-3)^2 + (-3)^2)
= √(9 + 9)
= √18
Now let's calculate the distance between points A' and B':
A'B' = √((2-3)^2 + (2-3)^2)
= √((-1)^2 + (-1)^2)
= √(1 + 1)
= √2
The scale factor is given by the ratio of the distances after and before dilation:
Scale factor = A'B' / AB
= (√2) / (√18)
= (√2) / (√(9 * 2))
= (√2) / (√9 * √2)
= (√2) / (3 * √2)
= 1 / 3
Therefore, the scale factor used in the dilation of line AB is 1/3.
The correct answer is c) 1/3.