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 smaller than 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 smaller than 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 as large as triangle ABC
and is 5 times closer to the center point of dilation.

Answer 1

When a triangle undergoes a dilation with a scale factor of 5 and a center of dilation at the origin (0, 0), the resulting triangle (let's call it triangle A′B′C′) will have certain characteristics based on the properties of dilation.

Dilation enlarges the shape while maintaining its proportions. Here are the specific changes expected:

1. The new triangle (A′B′C′) will be 5 times as large as the original triangle (ABC) in terms of each of its dimensions (lengths of sides, area, etc.).
2. Every point of triangle A′B′C′ will be 5 times as far from the origin (0, 0) as the corresponding point in triangle ABC.

Therefore, the correct description 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.