Question

Find the ratio in which the line segment joining the points $(2, 4, 5)$ and $(3, 5, -4)$ is divided by the $xz$-plane.

• A. $4:5$ externally
• B. $2: 3$ externally
• C. $1:3$ externally
• D. $4: 5$ internally

Answer 1

Answer: (A)

$4:5$ externally

Answer 2

Let the join of $P(2, 4, 5)$ and $Q(3, 5, -4)$ be divided by $xz$-plane in the ratio $k : 1$ at the point $R(x, y, z)$. Therefore $x = \frac{3k+2}{k+1}$, $y=\frac{5k+4}{k+1}$, $z=\frac{-4k+5}{k+1}$ Since the point $P\left(x,y, z\right)$ lies on $xz$-plane, the $y$-coordinate should be zero, i.e., $\frac{5k+4}{k+1}=0$ $\Rightarrow k =-\frac{4}{5}$ Hence, the required ratio is $-4 : 5$, i.e., the ratio is $4:5$ externally.