Question

If the co-ordinates of the midpoints of the sides of a triangle are $(1,1),(2,-3)$ and $(3,4)$, then the centroid of the triangles is ______.

• A. $(3,\frac{1}{3})$
• B. $(1,\frac{2}{3})$
• C. $(3,1)$
• D. $(2,\frac{2}{3})$

Answer 1

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

Let $(X_1,Y_1),(X_2,Y_2),(X_3,Y_3)$ be the mid points of sides of triangle ABC

then co-ordinates of centroid are given by :

$x=\frac{X_1+X_2+X_3}{3}$

$y=\frac{Y_1+Y_2+Y_3}{3}$

Now as per the question

then co-ordinates of centroid are

$x=\frac{1+2+3}{3}=2$

$y=\frac{1-3}{+}43=\frac{2}{3}$

$(2,\frac{2}{3})$ is co-ordinates of centroid.