Given:
The vertices of the triangle are given:
[tex]S(-2\text{ ,3) , T(6,7), U(4,1)}[/tex]The objective is to find the coordinates of the centroid of the triangle.
Now
The coordiantes of the centroid are given by:
[tex]=(\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3})[/tex]The vertices are :
[tex]\begin{gathered} (x_1,y_1)=(-2,3) \\ (x_2,y_2)=(6,7) \\ (x_3,y_3)=(4,1) \end{gathered}[/tex]The coordinates of centroid are:
[tex]\begin{gathered} =(\frac{-2+6+4}{3},\frac{3+7+1}{3}) \\ =(\frac{8}{3},\frac{11}{3}) \end{gathered}[/tex]This is the required answer.
