Question

The centroid of the triangle whose vertices are (2,-3);(4,6);(-2,8) is?​

Answer 1

Co-ordinates of centroid of triangle whose vertices are (a,b) , (c,d) and (e,f ) are :-

$\boxed{ \tt \bigg ( \dfrac{a + c + e}{3} , \dfrac{b+ d + f}{3} \bigg)}$

$\tt here : \\ \\ \rm a = 2 \\ \\ \rm b = - 3 \\ \\ \rm c = 4 \\ \\ \rm d = 6 \\ \\ \rm e= - 2 \\ \\ \rm f= 8$

$\tt \longrightarrow \bigg ( \dfrac{2+ 4 - 2}{3} , \dfrac{ - 3+ 6 + 8}{3} \bigg) \\ \\ \tt \longrightarrow \bigg ( \dfrac{ 4 }{3} , \dfrac{ 11}{3} \bigg)$

The centroid of the triangle whose vertices are (2,-3);(4,6);(-2,8) = (4/3 , 11/3 )

Additional-Information :-

Co-ordinates of midpoint of line joining (a,b) and (c,d) is given as :-

$\boxed{\rm \bigg( \dfrac{a + c}{2} \: , \: \dfrac{b + d}{2} \bigg)}$