Describe the dilation of triangle ABC

Question

, with a scale factor of 5 and a center point of dilation at the origin (0, 0)
. (1 point)
Responses

Triangle A′B′C′
is 5 times as large as triangle ABC
and is 5 times as far from the center point of dilation.
Triangle upper A prime upper B prime upper C prime is 5 times as large as triangle upper A upper B upper C and is 5 times as far from the center point of dilation.

Triangle A′B′C′
is 5 times as large as triangle ABC
and is 5 times closer to the center point of dilation.
Triangle upper A prime upper B prime upper C prime is 5 times as large as triangle upper A upper B upper C and is 5 times closer to the center point of dilation.

Triangle A′B′C′
is 5 times smaller than triangle ABC
and is 5 times as far from the center point of dilation.
Triangle upper A prime upper B prime upper C prime is 5 times smaller than triangle upper A upper B upper C and is 5 times as far from the center point of dilation.

Triangle A′B′C′
is 5 times smaller than triangle ABC
and is 5 times closer to the center point of dilation.

Answer 1

The correct description of the dilation of triangle ABC with a scale factor of 5 and a center point of dilation at the origin (0, 0) is:

Triangle A′B′C′ is 5 times as large as triangle ABC and is 5 times as far from the center point of dilation.

In dilations, when the scale factor is greater than 1, the resulting shape (A′B′C′) becomes larger than the original shape (ABC), and its vertices move away from the center of dilation, which in this case is the origin. Thus, with a scale factor of 5, each side of triangle A'B'C' will be 5 times the length of the corresponding side of triangle ABC, and the vertices of triangle A'B'C' will be 5 times farther from the origin than those of triangle ABC.