Question

Consider a $△ABC,$ whose vertices are $A(-2,3,-4),B(4,2,1)$ and $C(1,1,0),$ then the distance (in units) of its centroid from origin is

• A. $2$
• B. $\sqrt{6}$
• C. $4$
• D. $2\sqrt{5}$

Answer 1

The correct option is B $\sqrt{6}$

Given : vertices are $A(-2,3,-4),B(4,2,1)$ and $C(1,1,0),$
So, centroid $G\equiv (\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3},\frac{z_1+z_2+z_3}{3})$
$\Rightarrow G\equiv (\frac{-2+4+1}{3},\frac{3+2+1}{3},\frac{-4+1+0}{3})$
$\Rightarrow G\equiv (1,2,-1)$
and its distance from origin $=\sqrt{1^2+2^2+1^2}=\sqrt{6}$ units.