To determine the effect of the dilation of the parallel lines EF and GH with a scale factor of 16 and a center of dilation at the origin (0,0), we first need to calculate the coordinates of the resulting points after dilation.
The formula for dilation centered at the origin with a scale factor k is: \[ (x', y') = (k \cdot x, k \cdot y) \]
For line EF:
- Point E(-6, 6): \[ E' = (16 \cdot -6, 16 \cdot 6) = (-96, 96) \]
- Point F(-12, 12): \[ F' = (16 \cdot -12, 16 \cdot 12) = (-192, 192) \]
For line GH:
- Point G(-6, -6): \[ G' = (16 \cdot -6, 16 \cdot -6) = (-96, -96) \]
- Point H(-12, 0): \[ H' = (16 \cdot -12, 16 \cdot 0) = (-192, 0) \]
Now, let's summarize the results:
- E'(-96, 96)
- F'(-192, 192)
- G'(-96, -96)
- H'(-192, 0)
The dilated lines EF and GH are still parallel to each other since they have been scaled from their original positions while maintaining their relative orientation and distance from the center of dilation.
Each point has moved further away from the origin by a factor of 16, so the distance from the center of dilation has multiplied. Hence, we cannot say that the lines are only "six units farther" or "closer" but that they have scaled according to the factor.
Therefore, the correct response based on the calculations is: After dilation, the lines are farther from the point of dilation. The resulting points are E'(-96, 96), F'(-192, 192), G'(-96, -96), and H'(-192, 0). The dilated lines are parallel.