Question

Line AB
and line CD
are parallel lines. Line AB
contains the points A(1,4)
and B(2,2)
, and line CD
contains the points C(2,5)
and D(3,3)
. Describe the effect of the dilation with a scale factor of 4 and a center point of dilation at the origin (0,0)
.

Option #1: After dilation, the lines are four units farther from the point of dilation. The resulting points are A′ (5,8)
, B′ (6,6)
, C′(6,9)
, and D′(7,7)
.
Option #2: After dilation, the lines are four units farther from the point of dilation. The resulting points are A′ (4,16)
, B′ (8,8)
, C′(8,20)
, and D′(12,12)
.
Option #3: After dilation, the lines are four units closer to the point of dilation. The resulting points are A′ (1/4,1)
, B′ (1/2,1/2)
, C′(1/2,5/4)
, and D′(3/4,3/4)
.

(1 point)
Option #

Answer 1

Option #2.

Dilation with center (0,0) and scale factor 4 multiplies each coordinate by 4, so A(1,4)→(4,16), B(2,2)→(8,8), C(2,5)→(8,20), D(3,3)→(12,12). The lines remain parallel and are four times as far from the origin.