The line segment joining points (−3, −4), and (1, −2) is divided by y-axis in the ratio
(a) 1 : 3
(b) 2 : 3
(c) 3 : 1
(d) 2 : 3
Let $\mathrm{P}(0, y)$ be the point of intersection of $y$-axis with the line segment joining $\mathrm{A}(-3,-4)$ and $\mathrm{B}(1,-2)$ which divides the line segment $\mathrm{AB}$ in the ratio $\lambda: 1$.
Now according to the section formula if point a point $P$ divides a line segment joining $A\left(x_{1}, y_{1}\right)$ and $B\left(x_{2}, y_{2}\right)$ in the ratio m:n internally than,
$\mathrm{P}(x, y)=\left(\frac{m_{1}+m x_{2}}{m+n}, \frac{m y_{1}+m y_{2}}{m+n}\right)$
Now we will use section formula as,
$(0, y)=\left(\frac{\lambda-3}{\lambda+1}, \frac{-2 \lambda-4}{\lambda+1}\right)$
Now equate the x component on both the sides,
$\frac{\lambda-3}{\lambda+1}=0$
On further simplification,
$\lambda=3$
So $y$-axis divides $\mathrm{AB}$ in the ratio $\frac{3}{1}$
So the answer is (c)
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