Question

Angle ABC
contains the points A(−5,3)
, B(−4,−2)
, and C(1,4)
. Describe the effect of the dilation of the angle with a scale factor of 8 and a center point of dilation at the origin (0,0)
.(1 point)

After dilation, the angle is eight times farther from the point of dilation. The angle measurement remains the same. Corresponding lines (rays) are parallel between the angle and the dilated angle. The resulting points are A′(3,11)
, B′(4,6)
, and C′(9,12)
.

After dilation, the angle is eight times closer to the point of dilation. The angle measurement remains the same. Corresponding lines (rays) are parallel between the angle and the dilated angle. The resulting points are A′(−40,24)
, B′(−32,−16)
, and C′(8,32)
.

After dilation, the angle is eight times farther from the point of dilation. The angle measurement remains the same. Corresponding lines (rays) are parallel between the angle and the dilated angle. The resulting points are A′(−40,24)
, B′(−32,−16)
, and C′(8,32)
.

After dilation, the angle is eight times closer to the point of dilation. The angle measurement remains the same. Corresponding lines (rays) are parallel between the angle and the dilated angle.The resulting points are A′(−5/8,3/8)
, B′(−1/2,−1/4)
, C′(1/8,1/2)
.

Answer 1

The correct choice is the third one.

Because the dilation is centered at (0,0) with scale factor 8, each coordinate is multiplied by 8:
A' = 8(−5,3) = (−40,24), B' = 8(−4,−2) = (−32,−16), C' = 8(1,4) = (8,32).
The image is eight times farther from the center, the angle measure is unchanged, and corresponding rays are parallel.