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If $A(x_1,y_1) , B(x_2,y_2) , C(x_3,y_3)$ be the vertices of a triangle then prove that coordinates of centroid are given by $(\frac{(x_1 + x_2 + x_3)}3 , \frac{(y_1 + y_2 + y_3)}3)$

Slow learner
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    I assume you are defining the centroid as the intersection of the medians. If a median is $AM$ and the median is $G$, do you know that $AG=2GM$? If so, the question is easy. You take the coordinates of $M$, then $G$. – almagest Jan 19 '20 at 20:57
  • You need to know that if you have points $A(a,b)$ and $C(c,d)$ then the point $D$ on the line between $A$ and $C$ such that $AD:DC=h:k$ is $\frac{k}{h+k}(a,b)+\frac{h}{h+k}(c,d)$. Note that if $D$ is close to $A$ then $h<k$ but you want more of the $A$ coordinate, so make sure you get $h,k$ the right way round. – almagest Jan 19 '20 at 21:10
  • I got it. Thanks for hints. – Slow learner Jan 22 '20 at 04:44

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