Question

Describe the dilation of triangle ABC
𝐴
𝐵
𝐶
, with a scale factor of 5 and a center point of dilation at the origin (0, 0)
(
0
,

0
)
. (1 point)
Responses

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

Answer 1

To describe the dilation of triangle ABC with a scale factor of 5 and a center point of dilation at the origin (0, 0), we need to understand what dilation means in a geometric context.

1. **Scale Factor**: A scale factor of 5 means that each side of triangle ABC will be multiplied by 5. The dimensions of triangle \( A'B'C' \) will be 5 times larger than triangle \( ABC \).

2. **Center of Dilation**: The center of dilation is the point (0, 0) in this case. When a triangle is dilated from the origin, each vertex of the triangle is moved away from the origin by a distance that is proportional to its original distance from the origin.

Given these principles, the correct description of triangle \( A'B'C' \) after dilation 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.**

This means that if the original triangle ABC had vertices located at certain coordinates, the new triangle \( A'B'C' \) will have its vertices located at coordinates that are 5 times further from the origin than the original.