To find the coordinates of the points A' and B' after a dilation with a scale factor of \(\frac{1}{2}\) centered at the origin, we use the formula for dilation:
\[ (x', y') = (kx, ky) \]
where \( k \) is the scale factor, and \( (x, y) \) are the original coordinates of the point.
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For point A (-6, 4):
Using the scale factor \( k = \frac{1}{2} \):
\[ A' = \left(\frac{1}{2} \cdot -6, \frac{1}{2} \cdot 4\right) = \left(-3, 2\right) \]
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For point B (-8, 2):
Using the same scale factor \( k = \frac{1}{2} \):
\[ B' = \left(\frac{1}{2} \cdot -8, \frac{1}{2} \cdot 2\right) = \left(-4, 1\right) \]
Therefore, the coordinates after the dilation are:
- \( A' = (-3, 2) \)
- \( B' = (-4, 1) \)
Final results:
- \( A' = (-3, 2) \)
- \( B' = (-4, 1) \)