Question

The ratio in which the line segment joining the points A(−3, 2) and B(6, 1) is divided by the y-axis is

(a) 3 : 1
(b) 1 : 3
(c) 2 : 1
(d) 1 : 2

Answer 1

(d) 1 : 2

Let the y - axis cut the line segment joining A(- 3, 2) and B(6, 1) at the point P in the ratio k : 1.
Then, by section formula, the co-ordinates of P are
$\left(\frac{6k-3}{k+1},\frac{k+2}{k+1}\right)$
But P lies on the y-axis. So, its abscissa is 0.
∴ $$\begin{gathered} \frac{6k-3}{k+1}=0 \\ \Rightarrow 6k-3=0\Rightarrow 6k=3\Rightarrow k=\frac{3}{6}=\frac{1}{2} \end{gathered}$$
So, the required ratio is $\frac{1}{2}:1$, which is 1 : 2.