Question

in a triangle ABC A=(5,8)D is the midpoint of the side BC d=(2,-1).find the centroid of triangle ABC ​

Answer 1

$\textbf{Concept:}$

$\text{The centroid of triangle divides each median in the ratio 2:1}$

$\textbf{Formula used:}$

$\boxed{\begin{minipage}{8cm}\textbf{The coordinates of the point which divides the line segment joining} \bf(x_1,y_1)\:\textbf{and}\bf(x_2,y_2)\textbf{internally in the ratio m:n is}\\\\\bf(\frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n})\end{minipage}}$

$\textbf{Given:}$

$\text{In \triangle ABC, A(5,8) and}$

$\text{The midpoint of BC, D(2,-1)}$

$\text{Let G be the centroid of \triangle ABC}$

$\text{Then, G divides the median AD in the ratio 2:1}$

$\implies\text{G is}\;(\frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n})$

$\implies\text{G is}\;(\frac{2(2)+1(5)}{2+1},\frac{2(-1)+(8)}{2+1})$

$\implies\text{G is}\;(\frac{9}{3},\frac{6}{3})$

$\implies\textbf{G is}\bf(3,2)$

Find more:

Find the third vertex of a triangle, if two of its vertices are at (-3, 1) and (0, -2) and the centroid is at the origin.

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