line 1. A(9, 9) by B (6, 6)
line 2. A(3, 3) by B(2, 2)
determine the scale factor used in the dilation of line segment AB centered at the origin
1. 3
2. 1/3
3. -1/3
4.-3
To find the scale factor used in the dilation, we need to calculate the ratio of the lengths of the dilated line segments to the original line segments.
For line 1, the original line segment AB has a length of sqrt((9-6)^2 + (9-6)^2) = sqrt(18) = 3sqrt(2). The dilated line segment AB' has a length of sqrt((3*9-3*6)^2 + (3*9-3*6)^2) = sqrt(9) = 3.
The scale factor for line 1 is 3/3sqrt(2) = 1/sqrt(2) = sqrt(2)/2.
For line 2, the original line segment AB has a length of sqrt((3-2)^2 + (3-2)^2) = sqrt(2). The dilated line segment AB' has a length of sqrt((3*3-2*2)^2 + (3*3-2*2)^2) = sqrt(5).
The scale factor for line 2 is sqrt(5)/sqrt(2) = sqrt(10)/2.
Therefore, the scale factor used in the dilation of line segment AB centered at the origin is sqrt(2)/2 for line 1 and sqrt(10)/2 for line 2.
None of the given options (1, 1/3, -1/3, -3) match the calculated scale factors, so none is the correct answer.