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 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 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 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.

Question

GPT-4o mini · Answer

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 should consider how dilation works in geometry.

When we dilate a figure with a scale factor greater than 1, the new figure will be larger than the original figure. The vertices of the new triangle A′B′C′ will be positioned further away from the center of dilation (the origin in this case) than the original triangle ABC's vertices.

For a scale factor of 5, this means that the distances from each vertex of triangle ABC to the origin will be multiplied by 5. Therefore, triangle A′B′C′ is 5 times as large as triangle ABC and is 5 times as far from the center point of dilation (the origin).

Thus, the correct response 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.