Question

In what ratio does the x-axis divide the line segment joining the points (2,-3) and (5, 6)?

Answer 1

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

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

Given points are: $(2,-3),(5,6)$

Since, point is on $x-axis$, so $y$ coordinate is zero.

$\therefore 0=\frac{m\left(6\right)+n\left(-3\right)}{m+n}$

$0=6m-3n$

$6m=3n$

$\frac{m}{n}=\frac{3}{6}=\frac{1}{2}$

$\therefore m:n=1:2$