Fri February 25, 2011 By: Sneha George

"The centroid of a triangle divides each of the median in the ratio 2:1.." Can u plsss explain this sentence with the help of a diagram..??

Expert Reply
Fri February 25, 2011

Dear Student,

The centroid of a triangle is the point of intersection of its medians (the lines joining each vertex with the midpoint of the opposite side). The centroid divides each of the medians in the  ratio 2:1, which is to say it is located ⅓ of the perpendicular distance between each side and the opposing point (see figures). Its Cartesian coordinates are the means of the coordinates of the three vertices. That is, if the three vertices are a = (xa,ya), b = (xb,yb), and c = (xc,yc), then the centroid is



The centroid is therefore at \left(\frac13,\frac13,\frac13\right) in barycentric coordinates.

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