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a centroid separates a median into two segments. which of the following is the ratio of the length of the shorter segment to the length of the longer segment length

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The answer is 2:1.

The centroid separates the median, or the point from the midpoint of a side of a triangle with its opposite angle, at a ratio of 2:1, meaning that one segment is 1/3 the length of the median and the other segment is 2/3 the length of the median.
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