Question

Find the ratio in which the line segment $A(1,-5)$ and $B(-4,5)$ as divided by the $x$ axis. Also find the coordinates of the point of division.

Answer 1

Equation of line $AB=y+5$

$\frac{5+5}{-4-1}\left(x-1\right)$

$y+5=-2x-1)$

$y+5=-2x+2$

$y=-2x-3$

Now,

$AB$ meets $x-axis$ at $\left(\frac{-3}{2},0\right)$

$\left(\frac{\lambda -4}{\lambda +1},\frac{-5\lambda +5}{\lambda +1}\right)\equiv \frac{dy}{dx}\left(\frac{-3}{2},0\right)$

$\lambda =1$

$\frac{BC}{AC}=\frac{\lambda }{1}=1:1$

Hence, this is the answer.