Question

What will be the centroid of a triangle whose vertices are (2, 4), (6, 4) and (2, 0)?

• A. $\frac{8}{3},\frac{5}{3}$
• B. $\frac{7}{2},\frac{5}{2}$
• C. $\frac{10}{3},\frac{8}{3}$
• D. $\frac{4}{3},\frac{2}{3}$

Answer 1

The correct option is C $\frac{10}{3},\frac{8}{3}$

Centroid of a triangle with vertices $(x_1,y_1),(x_2,y_2)$ and $(x_3,y_3)$ is given by (x,y) where;

$x$ = $\frac{x_1+x_2+x_3}{3}$ and $y$ = $\frac{y_1+y_2+y_3}{3}$.

So, $x$ = $\frac{2+6+2}{3}$ = $\frac{10}{3}$ and

$y$ = $\frac{4+4+0}{3}$ = $\frac{8}{3}$

Therefore, the centroid is $(\frac{10}{3},\frac{8}{3})$