Question

Point $P$ divides the line segment joining the points $A(-1,3)$ and $B(9,8)$ such that $\frac{AP}{BP}=\frac{K}{1}$. If $P$ lies on the line $x-y+2=0,$ find the value of $k$.

Answer 1

It is given that P divides the line segment joining A(-1,3) and B(9,8) in the ratio k:1. so, coordinates of P are $(\frac{9k-1}{k+1},\frac{8k+3}{k+1})$.

$(\frac{9k-1}{k+1},\frac{8k+3}{k+1})$ lines on the line x-y+2=0

$\therefore \frac{9k-1}{k+1}-\frac{8k+3}{k+1}+2=0$

$\Rightarrow 9k-1-8k-3+2k+2=0$

$\Rightarrow 3k-2=0$

$\Rightarrow k=2/3$