Question

If the point P(1,2) lies on the line segments joining the point A(2,4) and B(4,8), then find$\frac{AP}{AB}$

Answer 1

REF. Image

Let P divide AB in k:1

$\Rightarrow 1=\frac{4k+2}{k+1}\Rightarrow 4k+2=k+1$

$\Rightarrow 3k=-1\Rightarrow k=-1/3$

$\Rightarrow$ P divides AB externally in 1:3 $\Rightarrow \frac{PA}{PB}=\frac{1}{3}$

$\Rightarrow 3PA=PB$

$\Rightarrow 3PA=PA+AB$

$\Rightarrow 2PA=AB\Rightarrow PA/AB=1/2$