Question

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

• A. $(1,2)$
• B. $(2,1)$
• C. $(-1,2)$
• D. $(1,-2)$

Answer 1

The correct option is A $(1,2)$

If $(x_1,y_1)$, $(x_2,y_2)$ and $(x_3,y_3)$ are the vertices of the triangle,

then the coordinates of its centroid are $(\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3})$

Here, it is given that the vertices of the triangle are $(3,1)$, $(2,3)$ and $(-2,2)$

therefore, the coordinates of centroid is given by:

$(\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3})=(\frac{3+2-2}{3},\frac{1+3+2}{3})=(\frac{3}{3},\frac{6}{3})=(1,2)$