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


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



(d) 1 : 2

Let $A B$ be divided by the $y$ axis in the ratio $k: 1$ at the point $P$.

Then, by section formula, the coordinates of are

$P\left(\frac{8 k-4}{k+1}, \frac{3 k+2}{k+1}\right)$

But, P lies on the y axis; so, its abscissa is 0

$\Rightarrow \frac{8 k-4}{k+1}=0$

$\Rightarrow 8 k-4=0$

$\Rightarrow 8 k=4$

$\Rightarrow k=\frac{1}{2}$

Hence, the required ratio is $\frac{1}{2}: 1$, which is same as $1: 2$.


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