To perform a dilation centered at the origin with a scale factor of \( \frac{1}{5} \), you multiply each coordinate of the vertices by the scale factor.
Given the original coordinates:
- \( F = (-5, -10) \)
- \( G = (0, -10) \)
- \( H = (5, 0) \)
We can calculate the dilated coordinates \( F' \), \( G' \), and \( H' \) as follows:
-
For \( F' \): \[ F' = \left( -5 \times \frac{1}{5}, -10 \times \frac{1}{5} \right) = \left( -1, -2 \right) \]
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For \( G' \): \[ G' = \left( 0 \times \frac{1}{5}, -10 \times \frac{1}{5} \right) = \left( 0, -2 \right) \]
-
For \( H' \): \[ H' = \left( 5 \times \frac{1}{5}, 0 \times \frac{1}{5} \right) = \left( 1, 0 \right) \]
So the coordinates of the vertices after the dilation are:
- \( F' = (-1, -2) \)
- \( G' = (0, -2) \)
- \( H' = (1, 0) \)