Question

The line segment joining $(2,-3)$ and $(5,6)$ is divided by x-axis in the ratio:

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

Answer 1

Answer: (C)

$1:2$

Using the section formula, if a point $(x,y)$ divides

the line joining the points $(x_1,y_1)$ and $(x_2,y_2)$ in the ratio $m:n$, then

$(x,y)=(\frac{m{x}_2+n{x}_1}{m+n},\frac{m{y}_2+n{y}_1}{m+n})$
Substituting $(x_1,y_1)=(2,-3)$ and $(x_2,y_2)=(5,6)$ in the section formula,

we get the point $(\frac{m\left(5\right)+n\left(2\right)}{m+n},\frac{m\left(6\right)+n(-3)}{m+n})$

Since the point of intersection lies on the x - axis, y - coordinate $=0$

$\frac{6m-3n}{m+n}=0$

$=>6m-3n=0$
$=>6m=3n$
$2m=n$
$=>m:n=1:2$