Question

In what ratio, $x$-axis divides the line segment which joins the points $\left(5,3\right)$ and $\left(-3,-2\right)$ ?

Answer 1

We know that by section formula, 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

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

Since, $(x_1,y_1)=(-3,-2)$ and $(x_2,y_2)=(5,3)$

$\therefore 0=\frac{m\left(3\right)+n(-2)}{m+n}$

$3m-2n=0$

$3m=2n$

$\frac{m}{n}=\frac{2}{3}$

$m:n=2:3$