Question

The vertices of a triangle are $(2,1),(5,2)$ and $(3,4)$. Then the co-ordinates of the centroid are

• A. $(10,3)$
• B. $(\frac{10}{3},7)$
• C. $(\frac{10}{3},\frac{7}{3})$
• D. $(\frac{7}{3},\frac{10}{3})$

Answer 1

The correct option is C $(\frac{10}{3},\frac{7}{3})$

We know that the coordinates of the centroid of triangle with vertices $A(x_1,y_1)$, $B(x_2,y_2)$ and $C(x_3,y_3)$ is

$(\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3})$

Thus the coordinates of the centroid of the triangle with the vertices $(2,1)$, $(5,2)$ and $(3,4)$ is

$(\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3})=(\frac{2+5+3}{3},\frac{1+2+4}{3})=(\frac{10}{3},\frac{7}{3})$