Find the ratio in which the x-axis cuts the join of the points A

Let the point which cuts the join of A(4, 5), and B(-10, -2) in the ratio k : 1 be P(x, 0)

Formula: If $k: 1$ is the ratio in which the join of two points is divided by another point $(x,$, y), then

$\mathrm{x}=\frac{\mathrm{kx}_{2}+\mathrm{x}_{1}}{\mathrm{k}+1}$

$\mathrm{y}=\frac{\mathrm{ky}_{2}+\mathrm{y}_{1}}{\mathrm{k}+1}$

Taking for the y co-ordinate,

$0=\frac{\mathrm{k} \times-2+5}{\mathrm{k}+1}$

$\Rightarrow 2 \mathrm{k}=5$

$\Rightarrow \mathrm{k}=\frac{5}{2}$

Therefore

$x=\frac{\frac{5}{2} \times-10+4}{\frac{5}{2}+1}$

$x=\frac{-50+8}{5+2}$

$x=\frac{-42}{7}$

$x=-6$

Therefore, the ratio in which $x$-axis cuts the join of the points $A(4,5)$ and $B(-10,-2)$ is 5 : 2and the point of intersection is $(-6,0)$.