Question

If the line $3x+4y=5$ divides the line segment joining the points $(1,2)$ and $(-2,3)$ in the rario $\lambda :1$, then the value of $|\lambda |$ is

Answer 1

Given ratio is $\lambda :1$
Points are $(1,2)$ and $(-2,3)$
Now, the required point
$=(\frac{1-2\lambda }{\lambda +1},\frac{3\lambda +2}{\lambda +1})$
Since this point lies on the line $3x+4y=5$
$3\left(\frac{1-2\lambda }{\lambda +1}\right)+4\left(\frac{3\lambda +2}{\lambda +1}\right)=5\Rightarrow 3-6\lambda +12\lambda +8=5\lambda +5\Rightarrow \lambda =-6\therefore |\lambda |=6$