The scale factor can be determined by finding the ratio of the distances between the corresponding points in the original and dilated lines.
The distance between A and B is given by the distance formula: sqrt((x2-x1)^2 + (y2-y1)^2)
So, the distance between A and B is sqrt((6-9)^2 + (6-9)^2) = sqrt(9+9) = sqrt(18)
Similarly, the distance between A' and B' is sqrt((2-3)^2 + (2-3)^2) = sqrt(1+1) = sqrt(2).
The scale factor can be found by dividing the distance of the dilated line by the distance of the original line:
Scale factor = sqrt(2) / sqrt(18)
Simplifying this, we get the scale factor as sqrt(2/18) = sqrt(1/9) = 1/3.
Therefore, the scale factor used in the dilation of line AB is 1/3.
A (9,9) B (6,6) A' (3,3) B' (2,2)
determine the scale factors used in the dilation of line AB with a center point of dilation at the origin
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