Question

The ratio in which $y-$ axis divides the line segment joining $(-3,5)$ and $(7,2)$ is

• A. $3:7$
• B. $2:7$
• C. $3:8$
• D. $3:5$

Answer 1

The correct option is A $3:7$

Given points are $(-3,5)$ and $(7,2)$
Let the ratio be $m:n$
Now, the required coordinates of point on $y-$ axis
$=(\frac{7m-3n}{m+n},\frac{2m+5n}{m+n})$

As the point lies on $y-$ axis, so $x$ coordinate will be zero, we get
$\frac{7m-3n}{m+n}=0$
$\Rightarrow 7m-3n=0$
$\therefore \frac{m}{n}=\frac{3}{7}$


Alternate method:
If coordinates of two points are $(x_1,y_1)$ and $(x_2,y_2)$
Let $y-$ axis divides it in ratio of $m:n$,
The $x-$ coordinate will be $0$.
$\frac{m{x}_2+n{x}_1}{m+n}=0\Rightarrow m{x}_2=-n{x}_1\Rightarrow \frac{m}{n}=-\frac{x_1}{x_2}$
Now, in our given question
$x_1=-3,x_2=7\therefore \frac{m}{n}=\frac{3}{7}$