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Barycenter for Three Masses at the Vertices of a Triangle

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For three masses: at , at , at , the barycenter (center of mass) is located at

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,

where .

The barycentric coordinates of the point with respect to the triangle are given by the ratios . This can be shown to equal the ratios of the triangle areas .

The tables show the equality of the normalized values of the masses and areas.

You can move the three vertices , and .

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Contributed by: S. M. Blinder (August 2022)
Open content licensed under CC BY-NC-SA

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