Question

Dilate the parallel lines EF
and GH
with a scale factor of 1/
6
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.(1 point)

After dilation, the lines are six units farther from the point of dilation. The resulting points are E′(−36,36)
, F′(−72,72)
, G′(−36,−36)
, and H′(−72,0)
.The dilated lines are parallel.

After dilation, the lines are six units farther from the point of dilation. The resulting points are E′(−1,1)
, F′(−2,2)
, G′(−1,−1)
, and H′(−2,0)
. The dilated lines are parallel.

After dilation, the lines are six units closer to the point of dilation. The resulting points are E′(−1,1)
, F′(−2,2)
, G′(−1,−1)
, and H′(−2,0)
. The dilated lines are parallel.

After dilation, the lines are six units farther from the point of dilation. The resulting points are E′(0,12)
, F′(−6,18)
, G′(0,0)
, and H′(−6,6)
. The dilated lines are parallel.

Answer 1

Correct choice: the third option.

Reason: A dilation with center (0,0) and scale factor 1/6 multiplies each coordinate by 1/6.
E' = (−6/6, 6/6) = (−1, 1)
F' = (−12/6, 12/6) = (−2, 2)
G' = (−6/6, −6/6) = (−1, −1)
H' = (−12/6, 0) = (−2, 0)

Distances from the origin are 1/6 of the originals, so the lines are six times closer to the origin and remain parallel.