Question

The ratio in which the line segment joining $(3,4)$ and $(-2,1)$ is divided by the y-axis is

• A. $1:2$
• B. $1:3$
• C. $3:2$
• D. None of these

Answer 1

The correct option is C $3:2$

Using the section formula, if a point $(x,y)$ divides the line joining the points $(x_1,y_1)$ and $(x_2,y_2)$ in the ratio $m:n$, then $(x,y)=(\frac{m{x}_2+n{x}_1}{m+n},\frac{m{y}_2+n{y}_1}{m+n})$

Let the ratio be $k:1$ now using section formula, we have:

$(x,y)=(\frac{k(-2)+1\left(3\right)}{k+1},\frac{k\left(1\right)+1\left(4\right)}{k+1})$
$(x,y)=(\frac{-2k+3}{k+1},\frac{k+4}{k+1})$
Since, line divided by y axis that means we have $x=0$
$0=\frac{-2k+3}{k+1}$ and $y=\frac{k+4}{k+1}$
$\Rightarrow 0\times (k+1)=-2k+3$
$\Rightarrow 0=-2k+3$
$\Rightarrow 2k=3$
$\therefore k=\frac{3}{2}$
Hence, the ratio is $k:1=3:2$