Question

In what ratio does $y$-axis divide the line segment joining points $P(5,7)$ and $Q(-8,9)$?

• A. $8:3$
• B. $5:8$
• C. $3:9$
• D. None of the above

Answer 1

The correct option is B $5:8$

Let the required ratio be $k:1=m:n$
Point on $y$- axis would be $(0,y)=(x,y)$

By Section Formula,

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

$0=\frac{k(-8)+1\left(5\right)}{k+1}$

$-8k+5=0$

$\therefore k=\frac{5}{8}$

Required ratio $k:1$$=\frac{5}{8}:1$ or $5:8$ (option $B$)