Question

The ratio in which the line joining $(2,4,5)$ and $(3,5,-4)$ is divided by the $YZ$-plane, is

• A. $2:3$
• B. $3:2$
• C. $-2:3$
• D. $4:-3$

Answer 1

Answer: (C)

Let the point $R$ divides the line joining the points $P(2,4,5)$ and $Q(3,5,-4)$ in the ratio $m:n$. Then, the coordinates of $R$ are $\left(\frac{3m+2n}{m+n},\frac{5m+4n}{m+n},\frac{-4m+5n}{m+n}\right)$.
For $yz$-plane, $x$-coordinates will be zero.
$\therefore \frac{3m+2n}{m+n}=0\Rightarrow \frac{m}{n}=\frac{-2}{3}$
Alternate Method
The ratio in which YZ-plane divides the line segment
$=-x_1:x_2=-2:3$