Question

The ratio in which a point $P(2,3)$ divides the line segment joining $A(-2,-7)$ and $B(4,8)$ is

• A. $1:2$
• B. $2:1$
• C. $1:3$
• D. $3:4$

Answer 1

The correct option is B $2:1$

Let the $P$ divides $AB$ in the ratio $\frac{\lambda }{1}$
$\frac{-2+4\lambda }{\lambda +1}=2\Rightarrow -1+2\lambda =\lambda +1$
$\Rightarrow \lambda =2$
$\frac{-7+8\lambda }{\lambda +1}=3\Rightarrow -7+8\lambda =3\lambda +3\Rightarrow \lambda =2\therefore \frac{AP}{PB}=\frac{2}{1}$