Question

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

• A. $3:2$
• B. $1:3$
• C. $4:3$
• D. $2:3$

Answer 1

The correct option is D $2:3$

Given points are $(3,-4)$ and $(-5,6)$
Let the ratio be $m:n$
Now, the required coordinates of point on $x-$ axis
$=(\frac{-5m+3n}{m+n},\frac{6m-4n}{m+n})$

As the point lies on $x-$ axis, so $y$ coordinate will be zero, we get
$\frac{6m-4n}{m+n}=0\Rightarrow 6m-4n=0\therefore \frac{m}{n}=\frac{2}{3}$



Alternate method:
If coordinates of two points are $(x_1,y_1)$ and $(x_2,y_2)$
$x-$ axis divides in ratio of
$\frac{m}{n}=-\frac{y_1}{y_2}$
Given coordinates are $y_1=-4,y_2=6$
$\therefore \frac{m}{n}=\frac{2}{3}$