The correct option is
B x1+x2+x33,y1+y2+y33The points
A(x1,y1),B(x2,y2) and
C(x3y3) are the vertices of
ΔABC.
Let the median AD meet BC at D.
To find: Co-ordinates of its centroid G(X,Y) .
G(X,Y) of ΔABC will divide its median AD in the ratio m:n=2:1
i.e AG:GD=2:1 when D(x4,y4) is the mid-point of BC.
So, the co-ordinates of D(x4,y4), by the section formula for mid point, are
D(x4,y4)=(x3+x22,y3+y22).
∴ the co-ordinates of G(X,Y) by the section formula is,
X=nx1+nx4m+n=x1+x32×2+x2×12+1=x1+x2+x33 and
Y=ny1+ny4m+n=y1+y32×2+y2×12+1=y1+y2+y33
∴G(X,Y)=(x1+x2+x33,y1+y2+y33)
The co-ordinates of the centroid G(X,Y)=(x1+x2+x33,y1+y2+y33)
![140862_81269_ans.png](https://search-static.byjusweb.com/question-images/toppr_ext/questions/140862_81269_ans.png)