SSC CGL Model Paper 8

Let the point on y-axis be P(0, y) ( ∵ on y-axis, x = 0)
Let the y-axis divides the segment joining (-1 ,3 ) and (2, - 4) in the ratio m : n. $\left(0,\mathit{y}\right)=\left(\frac{\mathit{m}{\mathit{x}}_2+\mathit{n}{\mathit{x}}_1}{\mathit{m}+\mathit{n}},\frac{\mathit{m}{\mathit{y}}_2+\mathit{n}{\mathit{y}}_1}{\mathit{m}+\mathit{n}}\right)$
$=\left(\frac{\mathit{m}\left(2\right)+\mathit{n}\left(-1\right)}{\mathit{m}+\mathit{n}},\frac{\mathit{m}\left(-4\right)+\mathit{n}\left(3\right)}{\mathit{m}+\mathit{n}}\right)$
Comparing the both sides,
$\frac{2\mathit{m}-\mathit{n}}{\mathit{m}+\mathit{n}}=0$
⇒ 2m = n
⇒ $\frac{\mathit{m}}{\mathit{n}}=\frac{1}{2}$
∴ $\mathit{m}:\mathit{n}=1:2$