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I've done it the way you mentioned but I don't see how that proves the mean of the 3 vertices is equal to the center of mass.

thanks

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\begin{cases}

x_A + (x_B - x_A + x_C - x_A)s/2 = x_B + (x_A - x_B + x_C - x_B)t/2

\\y_A + (y_B - y_A + y_C - y_A)s/2 = y_B + (y_A - y_B + y_C - y_B)t/2

\end{cases}

[/tex]And this is solved with [tex]\begin{cases}s = 2/3 \\ t = 2/3\end{cases}[/tex](Show it.)

This means that the centroid lies at 2/3 along any median. Taking one of the equations of the medians, and substituting s or t in it, we obtain the coordinates of the centroid: [tex] (\frac {x_A + x_B + x_C} 3, \frac { y_A + y_B + y_C } 3) [/tex]

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