Question

The ratio in which the line joining the points $(3,-4)$ & $(-5,6)$ is divided by x-axis.

Answer 1

We know that if a line joining the points $A\left(x_1{y}_1\right)$ and

B$(x_2,y_2)$ is divided by a point O(x,y) in

the ratio m:n,

then $x=\frac{m{x}_2+n{x}_1}{m+n}$

and

$y=\frac{m{y}_2+n{y}_1}{m+n}$

Hence $A(3,-4)$ & $B(-5,6)$ are points on a line which is divided by a point on x-axis, then the coordinates of the point will be $C(x,0).$

Since the point lies on $x$ axis its $y$ coordinate is $0$

Let $C$ divide live joining $AB$ in the ratio $k:1$

$\Rightarrow 0=\left(\frac{k\times 6+1\times -4}{k+1}\right)$

$\Rightarrow$ 6k-4=0

$\Rightarrow 6k=4$

$\Rightarrow k=\frac{2}{3}$

Hence the ratio in which x axis divide line joining points $AB$ is $2:3$