To find the coordinates of the vertices after a dilation with a scale factor of \( \frac{1}{2} \) centered at the origin, you multiply each coordinate by the scale factor.
The original coordinates are:
- A = (-6, -8)
- B = (-6, -2)
- C = (-2, 8)
- D = (-2, -8)
Now we will apply the scale factor of \( \frac{1}{2} \):
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For A' : \[ A' = \left(-6 \times \frac{1}{2}, -8 \times \frac{1}{2}\right) = \left(-3, -4\right) \]
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For B' : \[ B' = \left(-6 \times \frac{1}{2}, -2 \times \frac{1}{2}\right) = \left(-3, -1\right) \]
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For C' : \[ C' = \left(-2 \times \frac{1}{2}, 8 \times \frac{1}{2}\right) = \left(-1, 4\right) \]
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For D' : \[ D' = \left(-2 \times \frac{1}{2}, -8 \times \frac{1}{2}\right) = \left(-1, -4\right) \]
Now we can list the coordinates of the vertices after the dilation:
- A' = (-3, -4)
- B' = (-3, -1)
- C' = (-1, 4)
- D' = (-1, -4)
So the final coordinates are:
- A' = (-3, -4)
- B' = (-3, -1)
- C' = (-1, 4)
- D' = (-1, -4)