To find the coordinates of the points A' and B' after a dilation centered at the origin with a scale factor of \( \frac{1}{2} \), we apply the dilation transformation to each endpoint. The transformation for a point \( (x, y) \) under dilation with a scale factor \( k \) is given by:
\[ (x', y') = (k \cdot x, k \cdot y) \]
Here, the scale factor \( k \) is \( \frac{1}{2} \).
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For point A (-6, 4): \[ A' = \left(\frac{1}{2} \cdot -6, \frac{1}{2} \cdot 4\right) = \left(-3, 2\right) \]
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For point B (-8, 2): \[ B' = \left(\frac{1}{2} \cdot -8, \frac{1}{2} \cdot 2\right) = \left(-4, 1\right) \]
Thus, the coordinates after dilation are:
- \( A' (-3, 2) \)
- \( B' (-4, 1) \)
In conclusion:
- \( A' (-3, 2) \)
- \( B' (-4, 1) \)