Question

In what ratio is the line segment joining the points $(4,6)$ and $(-7,-1)$ is divided by $X$-axis ?

• A. $1:6$
• B. $6:2$
• C. $2:6$
• D. $6:1$

Answer 1

The correct option is A $1:6$

We know that, the co-ordinates of the points which divide internally the line segment joining the points $(x_1,y_1)$ and $(x_2,y_2)$ in the ratio $m:n$ is

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

Given two points $A(4,6)$ and $B(-7-1)$

Let the coordinate of the point on X-axis be $(x,o)$ where it meets AB and the ratio be $m:n$ in which it divides AB.

By section formula:

$x=\left(\frac{m{x}_2+n{x}_1}{m+n}\right),y=\left(\frac{m{y}_2+n{y}_1}{m+n}\right)\text{Here}y=\frac{-m+6n}{m+n}\Rightarrow x=\frac{-7+4n}{m+n}$

$0=\frac{-m+6n}{m+n}\therefore -m+6n=0\Rightarrow m=6n\therefore m:n=1:6$