Question

In what ratio does the y-axis divide the join of P(−4, 2) and Q(8, 3)?

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

Answer 1

(d) 1 : 2
Let AB be divided by the y axis in the ratio $k:1$ at the point P.
Then, by section formula, the coordinates of P are
$P\left(\frac{8k-4}{k+1},\frac{3k+2}{k+1}\right)$
But, P lies on the y axis; so, its abscissa is 0.
$\Rightarrow \frac{8k-4}{k+1}=0$
$\Rightarrow 8k-4=0$
$\Rightarrow 8k=4$
$\Rightarrow k=\frac{1}{2}$
Hence, the required ratio is $\frac{1}{2}:1$, which is same as 1 : 2.