Question

If $(4,2,p)$ is the centroid of the tetrahedron formed by the points $(k,2,-1),(4,1,1),(6,2,5)$ and
$(3,3,3)$ then $k+p=$

• A. $\frac{17}{3}$
• B. $1$
• C. $\frac{5}{3}$
• D. $5$

Answer 1

The correct option is D $5$

Centroid of the tetrahedron formed by the points $(k,2,-1),(4,1,1),(6,2,5)$ and $(3,3,3)$ is,

$=(\frac{k+4+6+3}{4},\frac{2+1+2+3}{4},\frac{-1+1+5+3}{4})=(\frac{k+13}{4},2,2)=(4,2,p)$ (given)

$\therefore \frac{k+13}{4}=4\Rightarrow k=3$

and $p=2$

Hence $k+p=3+2=5$