Question

The distance from the origin to the centroid of the tetrahedron formed by the points $(0,0,0),(a,0,0),(0,b,0),(0,0,c)$ is:

• A. $\frac{\sqrt{a+b+c}}{4}$
• B. $\frac{\sqrt{a+b+c}}{3}$
• C. $\frac{\sqrt{a^2+b^2+c^2}}{16}$
• D. $\frac{\sqrt{a^2+b^2+c^2}}{4}$

Answer 1

The correct option is D $\frac{\sqrt{a^2+b^2+c^2}}{4}$

Let centroid of the tetrahedron having vertices $(0,0,0),(a,0,0),(0,b,0)$ and $(0,0,c)$ be $G$.

So, coordinate of $G$ is given by,

$G=(\frac{0+a+0+0}{4},\frac{0+0+b+0}{4},\frac{0+0+0+c}{4})=(\frac{a}{4},\frac{b}{4},\frac{c}{4})$

Hence, distance of $G$ from origin is $=OG=\sqrt{{(\frac{a}{4}-0)}^2+{(\frac{b}{4}-0)}^2+{(\frac{c}{4}-0)}^2}=\frac{\sqrt{a^2+b^2+c^2}}{4}$