Question

The line segment joining the points $(3,5)$ and $(-4,2)$ is divided by $y$-axis in the ratio:

• A. $5:3$
• B. $3:5$
• C. $4:3$
• D. $3:4$

Answer 1

The correct option is D $3:4$

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 $(x,y)=(\frac{m{x}_2+n{x}_1}{m+n},\frac{m{y}_2+n{y}_1}{m+n})$
Substituting $(x_1,y_1)=(3,5)$ and $(x_2,y_2)=(-4,2)$ in the section formula, we get the point

$(\frac{m(-4)+n\left(3\right)}{m+n},\frac{m\left(2\right)+n\left(5\right)}{m+n})$

Since the point of intersection lies on the $y$-axis, $x$-coordinate $=0$

$\frac{-4m+3n}{m+n}=0$

$\Rightarrow -4m+3n=0$
$\Rightarrow 4m=3n$

$\Rightarrow m:n=3:4$