To find the scale factor used in the dilation of the line segment AB from point A(9, 9) to point A'(3, 3) and point B(6, 6) to point B'(2, 2), we can use the formula for dilation with respect to the origin.
The scale factor \( k \) with the origin as the center of dilation can be calculated using the following formula:
\[ k = \frac{\text{new coordinate}}{\text{old coordinate}} \]
Let's calculate the scale factor using point A and A'.
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For point A(9, 9) to A'(3, 3): \[ k = \frac{3}{9} = \frac{1}{3} \]
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For point B(6, 6) to B'(2, 2): \[ k = \frac{2}{6} = \frac{1}{3} \]
Since both points A and B yield the same scale factor, we conclude that the scale factor for the dilation is:
\[ \frac{1}{3} \]
Thus, the answer is:
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