Question

The ratio in which the line joining (2, 4, 5) and (3, 5, -9) is divided by the

yz-plane is

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

Answer 1

The correct option is C -2 : 3

Let A = (2, 4, 5) and B = (3, 5, -9)

Let the line joining A and B be divided by the

yz-plane at point P in the ratio $\lambda$: 1

Then, we have

P = $(\frac{3\lambda +2}{\lambda +1},\frac{5\lambda +4}{\lambda +1},\frac{-9\lambda +5}{\lambda +1})$

Since P lies on the yz-plane, the x-coordinate of P will be zero.

$\therefore \frac{3\lambda +2}{\lambda +1}=0$

$\Rightarrow 3\lambda +2=0$

$\Rightarrow \lambda =\frac{-2}{3}$

Hence, the yz-plane divides AB in the ratio - 2 : 3