Question

The ratio, in which the line segment joining $(3,-4)$ and $(-5,6)$ is divided by the $x$-axis is

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

Answer 1

Answer: (B)

$2:3$

The given points are $A(3.-4)$ and $B(-5,6)$

Let the point of intersection be $P$

The point lies on $x$-axis, so it can be taken as $P=(x,0)$

Let $P$ divides $AB$ in the ratio $\lambda :1$

By Section Formula,

$\Rightarrow (x,0)=(\frac{\lambda \times (-5)+1\times 3}{\lambda +1},\frac{\lambda \times 6+1\times (-4)}{\lambda +1})$

Now,

$\frac{\lambda \times 6+1\times (-4)}{\lambda +1}=0$

$\Rightarrow \lambda \times 6+1\times (-4)=0$

$\Rightarrow 6\lambda -4=0$

$\Rightarrow 6\lambda =4$

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

Hence, the required ratio is $2:3$