Question

$G(1,1,-2)$ is the centroid of the triangle $ABC$ and $D$ is the mid point of $BC$. If $A=(-1,1,-4)$, then $D=$

• A. $\left(\frac{1}{2},1,\frac{-5}{2}\right)$
• B. $(5,1,2)$
• C. $(-5,-1,-2)$
• D. $(2,1,-1)$

Answer 1

Answer: (D)

$(2,1,-1)$

Let the coordinates of $D$ be $(p,q,r)$.
Since, the centroid divides the line joining $AD$ in the ratio $2:1$, the coordinates of centroid should be,
$(\frac{2p-1}{3},\frac{2q+1}{3},\frac{2r-4}{3})$
Comparing it with the coordinates of the centroid given, $D(2,1,-1)$.