Suppose a set of k arbitrary points, x_i, 1<=i<=k, x_i from R^2 are selected from a line. How can it be shown that a weighted barycenter x_o=(o_i*x_i)/(o_1+o_2+...+o_k) also belongs to that line (assume o_i are arbitrary weights)? Does the choice of weights restrict the solutions (ie, a particular choice to satisfy that x_o is within the 'convex hull' of other points)?(adsbygoogle = window.adsbygoogle || []).push({});

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# Weighted average of arbitrary k points from a line

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