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.
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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 \( ABC \).
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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.