Question

Find the coordinates of the points which trisect the line segment joining the points $P(4,2,-6)$ and $Q(10,-16,6)$.

• A. $(6-4,-2)$, $(8,10,-2)$
• B. $(6,-4,-2)$, $(8,-10,2)$
• C. $(6,-4,-2)$, $(8,-2,10)$
• D. $(6,-4,2)$, $(8,2,-10)$

Answer 1

Answer: (B)

Let $B$ and $S$ be two points which trisect the join of $PQ$.

$\because$ Point $R$ divides the join of $PQ$ in the ratio $1:2$
$\therefore$ Coordinates of $B$ is
$\left(\frac{1\times 10+2\times 4}{1+2},\frac{1\times \left(-16\right)+2\times 2}{1+2},\frac{1\times 6+2\times \left(-6\right)}{1+2}\right)$
$=\left(6,-4,-2\right)$
Also point $S$ divides the join of $PQ$ in the ratio $2:1$
$\therefore$ Coordinates of $R$ is
$\left(\frac{2\times 10+1\times 4}{1+2},\frac{2\times \left(-16\right)+1\times 2}{1+2},\frac{2\times 6+1\times \left(-6\right)}{1+2}\right)$
$=\left(8,-10,2\right)$.