To dilate the vertices of a shape in reference to the origin using a dilation factor, you multiply each coordinate of the vertices by the dilation factor.
In this case, the dilation factor is 3, and the vertices of the parallelogram are:
- E(-1, 5)
- F(2, 8)
- G(4, 4)
- H(1, 1)
Now, let's apply the dilation factor to each vertex:
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For vertex E(-1, 5): \[ E' = (3 \times -1, 3 \times 5) = (-3, 15) \]
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For vertex F(2, 8): \[ F' = (3 \times 2, 3 \times 8) = (6, 24) \]
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For vertex G(4, 4): \[ G' = (3 \times 4, 3 \times 4) = (12, 12) \]
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For vertex H(1, 1): \[ H' = (3 \times 1, 3 \times 1) = (3, 3) \]
Thus, the new coordinates of the vertices after dilation are:
- E'(-3, 15)
- F'(6, 24)
- G'(12, 12)
- H'(3, 3)
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