Question

If the line joining $A(1,3,4)$ and $B$ is divided by the point $(-2,3,5)$ in the ratio $1:3$, then $B$ is

• A. $(-11,3,8)$
• B. $(-11,3,-8)$
• C. $(-8,12,20)$
• D. $(13,6,-13)$

Answer 1

The correct option is A $(-11,3,8)$

Let the co-ordinates of $B$ be $(x,y,z)$.

Then applying the section formula gives us
$-2=\frac{3\left(1\right)+x}{3+1}$
$-8=x+3$
$x=-11$................(i)

Similarly $3=\frac{3\left(3\right)+y}{4}$
$12=9+y$
$y=3$ ..........(ii)
$5=\frac{3\left(4\right)+z}{4}$
$20=12+z$
$z=8$ ...........(iii)

Hence $B=(-11,3,8)$