Question

In what ratio is the line segment joining the point (-2,-3) and (3,7) divided by y-axis?

• A. $5:1$
• B. $1:5$
• C. $2:3$
• D. $3:2$

Answer 1

The correct option is C $2:3$

Let the required ratio be $k:1$ and the point on the y-axis be $(x,y)=(0,y)$

Section formula :

$(x,y)=(\frac{m{x}_2+n{x}_1}{m+n},\frac{m{y}_2+n{y}_1}{m+n})$

$(0,y)=(\frac{k{x}_2+x_1}{k+1},\frac{k{y}_2+y_1}{k+1})$

$\therefore x=\frac{k{x}_2+x_1}{k+1},0=\frac{k{y}_2+y_1}{k+1}$

Here $x_1=-2,y_1=-3$ and $x_2=3,y_2=7$

By Substituiting the values

$\Rightarrow 0=\frac{k\times 3+(-2)}{k+1}$

$\Rightarrow 0=3k-2$

$\Rightarrow -3k=-2$

$\Rightarrow k=\frac{2}{3}$

$\therefore$ Required Ratio = $2:3$