Question

Dilate the parallel lines EF and GH with a scale factor of 16 and a center point of dilation at the origin (0,0) . Line EF contains the points E(−6,6) and F(−12,12) . Line GH contains the points G(−6,−6) and H(−12,0) . Describe the effect of the dilation of the parallel lines.

Answer 1

[AI-generated answer — Bot GPT 3.5]

When we dilate the parallel lines EF and GH with a scale factor of 16 and a center point of dilation at the origin (0,0), the points E, F, G, and H will move away from the origin by a factor of 16.

The new coordinates for E and F will be:

E' = (-6 * 16, 6 * 16) = (-96, 96)
F' = (-12 * 16, 12 * 16) = (-192, 192)

The new coordinates for G and H will be:

G' = (-6 * 16, -6 * 16) = (-96, -96)
H' = (-12 * 16, 0 * 16) = (-192, 0)

Thus, the effect of the dilation is that the parallel lines EF and GH are stretched away from the origin, resulting in lines E'F' and G'H' that are 16 times longer and maintain the same distance between them.