Describe the dilation of triangle ABC

Question

Describe the dilation of triangle  ABC
 , 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 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.

GPT-4o mini · Answer

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 mathematical terms, when a figure is dilated from the origin with a scale factor greater than 1, the new figure becomes larger, with each vertex moving away from the center of dilation by a distance that is scaled by the factor. In this case, the scale factor is 5, so each side of triangle ABC becomes 5 times longer, and each point of the triangle moves 5 times further away from the origin.