Question

The coordinates of the vertices of a triangle are $(0,1),(2,3)$ and $(3,5)$. Find centroid of the triangle

• A. $(5,9)$
• B. $(\frac{5}{2},\frac{9}{2})$
• C. $(\frac{5}{3},3)$
• D. $(3,\frac{5}{3})$

Answer 1

The correct option is C $(\frac{5}{3},3)$

Let co-ordinates of a triangle are $A(x_1,y_1),B(x_2,y_2),C(x_3,y_3)$

Here, $A(0,1),B(2,3),C(3,5)$

Centro-id of the triangle $=(x_c,y_c)$

$x_c=\frac{x_1+x_2+x_3}{3}=\frac{0+2+3}{3}=\frac{5}{3}$

$y_c=\frac{y_1+y_2+y_3}{3}=\frac{1+3+5}{3}=3$

$\Rightarrow$ The centroid is $(\frac{5}{3},3)$