Question

Find the centroid of a triangle whose vertices are (2,3), (-4, 6) and (2, -6)

• A. $(0,1)$
• B. $(0,-1)$
• C. $(1,0)$
• D. $(-1,0)$
• E. none of these

Answer 1

The correct option is C $(1,0)$

Since, if $(x_1,y_1),(x_2,y_2)$ and $(x_3,y_3)$ are the vertices of a triangle. then centroid of the triangle is $(\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3})$
Vertices of a given triangle are $(2,3),(-4,6)$ and $(2,-6)$
$\therefore$ centroid $=(\frac{2+(-4)+2}{3},\frac{3+6+(-6)}{3})$
$=(\frac{0}{3},\frac{3}{3})$
$=(0,1)$
Option A is correct.