To determine the scale factor used in the dilation of line segment AB with a center point of dilation at the origin, we need to analyze the coordinates of the endpoints before and after dilation.
From the information you provided:
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Original Line AB has endpoints at:
- A(-6, 8)
- B(4, -8)
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Dilation Resulting Points are:
- A'(-3, 4)
- B'(2, -4)
The formula to find the scale factor \( k \) for the dilation is given by: \[ k = \frac{x'}{x} \] where \( (x, y) \) are the coordinates of the original point and \( (x', y') \) are the coordinates of the dilated point.
Let's calculate the scale factor:
For point A: \[ k = \frac{-3}{-6} = \frac{1}{2} \]
For point B: \[ k = \frac{2}{4} = \frac{1}{2} \]
Both points give the same scale factor.
Thus, the scale factor used in the dilation of line segment AB with the center point of dilation at the origin is \( \frac{1}{2} \).