To find the coordinates of A' and B' after a dilation with a scale factor of \( \frac{1}{2} \) centered at the origin, we apply the dilation formula. For a point \( (x, y) \), the new coordinates after dilation by a scale factor \( k \) are given by:
\[ (x', y') = (kx, ky) \]
Step 1: Find A' from A (-6, 4)
For point A (-6, 4):
\[ A' = \left(\frac{1}{2} \cdot -6, \frac{1}{2} \cdot 4\right) = \left(-3, 2\right) \]
Step 2: Find B' from B (-8, 2)
For point B (-8, 2):
\[ B' = \left(\frac{1}{2} \cdot -8, \frac{1}{2} \cdot 2\right) = \left(-4, 1\right) \]
Conclusion
The coordinates after the dilation are:
- \( A' = (-3, 2) \)
- \( B' = (-4, 1) \)