To perform a dilation centered at the origin with a scale factor of \(\frac{1}{5}\), you'll multiply each coordinate of the vertices by the scale factor.
The original coordinates are:
- \( F(-5, -10) \)
- \( G(0, -10) \)
- \( H(3, 0) \)
Now, we apply the scale factor of \(\frac{1}{5}\):
-
For point \( F \): \[ F' = \left(-5 \cdot \frac{1}{5}, -10 \cdot \frac{1}{5}\right) = \left(-1, -2\right) \]
-
For point \( G \): \[ G' = \left(0 \cdot \frac{1}{5}, -10 \cdot \frac{1}{5}\right) = \left(0, -2\right) \]
-
For point \( H \): \[ H' = \left(3 \cdot \frac{1}{5}, 0 \cdot \frac{1}{5}\right) = \left(\frac{3}{5}, 0\right) \]
Thus, the coordinates of the vertices after the dilation are:
- \( F'(-1, -2) \)
- \( G'(0, -2) \)
- \( H'\left(\frac{3}{5}, 0\right) \)