To find the coordinates of the vertices after a dilation with a scale factor of 2, centered at the origin, you multiply each coordinate of the vertices by the scale factor.
Given points:
- \( F(-4, 5) \)
- \( G(4, 5) \)
- \( H(-3, -4) \)
Now, apply the dilation:
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For point \( F \): \[ F' = (2 \cdot -4, 2 \cdot 5) = (-8, 10) \]
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For point \( G \): \[ G' = (2 \cdot 4, 2 \cdot 5) = (8, 10) \]
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For point \( H \): \[ H' = (2 \cdot -3, 2 \cdot -4) = (-6, -8) \]
Thus, the coordinates of the vertices after the dilation are:
- \( F'(-8, 10) \)
- \( G'(8, 10) \)
- \( H'(-6, -8) \)