To perform a dilation of the points with a scale factor of 14 from the origin (0,0), we multiply the coordinates of each point by the scale factor. Let's calculate the dilated coordinates for each of the given points.
For line EF:
- Point E(4, 4): \[ E' = (14 \times 4, 14 \times 4) = (56, 56) \]
- Point F(8, 8): \[ F' = (14 \times 8, 14 \times 8) = (112, 112) \]
For line GH:
- Point G(8, -4): \[ G' = (14 \times 8, 14 \times -4) = (112, -56) \]
- Point H(12, 0): \[ H' = (14 \times 12, 14 \times 0) = (168, 0) \]
Now, we have the following new points:
- E'(56, 56)
- F'(112, 112)
- G'(112, -56)
- H'(168, 0)
Now let's analyze the options:
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Option #1 states that the lines are 4 units closer to the point of dilation, which is incorrect as the lines are dilating outward.
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Option #2 suggests the lines are 4 units farther from the point of dilation, but the new points come to much larger values than given.
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Option #3 states that the lines are 4 units farther from the point of dilation, which matches the behavior of the dilation, but again gives incorrect coordinates.
None of the provided options accurately represent the result of the dilation with a scale factor of 14, as the resulting points are significantly larger than those listed in any option. Therefore, based on the calculations, you can conclude the proper result, though it does not correspond to any of the given options.
If forced to choose based on the behavior of dilation (moving farther away), Option #3 is the only one that aligns with the correct description of the effect, even though the points are not correct. Therefore, you may choose:
Option #3