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

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

Introduction to Three Dimensional Geometry

Solution:

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 $\left(\frac{3 m+2 n}{m+n}, \frac{5 m+4 n}{m+n}, \frac{-4 m+5 n}{m+n}\right)$.
For $y z$-plane, $x$-coordinates will be zero.
$\therefore \frac{3 m+2 n}{m+n}=0 \Rightarrow \frac{m}{n}=\frac{-2}{3}$
Alternate Method
The ratio in which YZ-plane divides the line segment
$=-x_1: x_2=-2: 3$