三角形重心向量公式 三角形重心公式向量形式
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1、设A(x1，y1)，B(x2，y2)，C(x3，y3)，再设BC中点为D，重心G是中线上的一个三等分点，所以AG=2GD，D的坐标是((x2+x3)/2，(y1+y2)/2)，再设G(x，y)，所以AG=(x-x1，y-y1)，GD=((x2+x3)/2-x，(y2+y3)/2-y)，代入AG=2GD，可以解得：x=(x1+x2+x3)/3，y=(y1+y2+y3)。
2、因为D是BC中点，所以可以知道，2GD=GB+GC，同时因为AG=2GD，所以AG=GB+GC，即GA+GB+GC=0。
因为GA+GB+GC=0，设坐标原点为O，所以GA=OA-OG，GB=OB-OG，GC=OC-OG。所以3OG=OA+OB+OC，然后重心坐标公式自己证明吧，OG=(OA+OB+OC)/3。
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