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 $3:2$

Let $A(3,4)$ and $B(-2,1)$ be the two points

Taking the ratio as $k:1$ in which the point $P$ divides, we have the co-ordinates to be $[\frac{k{x}_2+x_1}{k+1},\frac{k{y}_2+y_1}{k+1}]$

According to coordinates , point A is $3$ units from the y-axis in the positive direction .Similarly point B is $2$ units from the y-axis in the negative direction.

$[\frac{k(-2)+3}{k+1},\frac{k\left(1\right)+\left(4\right)}{k+1}]$ = $(0,y)$

On solving we get $k=\frac{3}{2}$

$\therefore$ y-axis divides the line AB in the ratio $3:2$

$\therefore$ Ratio $=3:2$