Question

If the coordinates of the midpoints of the sides of a triangle are $(1,1),(2,-3)$ and $(3,4)$. Find the centroid.

• A. $(2,\frac{2}{3})$
• B. $(3,\frac{2}{3})$
• C. $(4,\frac{2}{3})$
• D. None of these

Answer 1

The correct option is A $(2,\frac{2}{3})$

if coordinates of mid pt.of sides are $(x_1,y_1),(x_2,y_2)$

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

$\Rightarrow G=(\frac{1+2+3}{2},\frac{1-3+4}{3})\Rightarrow G=(2,\frac{2}{3})$