Question

If $2x+4y+1=0$ is right angle bisector of line segment joining $(k,1)$ and $(2,\mu )$ then find $\left(\mu \right)$ and k

Answer 1

since $O$ is the midpoint of $AB$

$O\left(\frac{k+2}{\alpha },\frac{\mu +1}{2}\right)$
This point satisfy the line $2x+4y+1=0$

$\begin{array}{c}2\left(\frac{k+2}{\alpha }\right)+4\left(\frac{\mu +1}{2}\right)+1=0\\ k+2+2\mu +2+1=0\\ k+2\mu +5=\mathrm{0.....}\left(1\right)\\ \frac{\mu -1}{2-k}=2\\ \mu -1=4-2k\\ \mu +2k=\mathrm{5.....}\left(2\right)\end{array}$

By $\left(1\right)$ an $\left(2\right)$

$\begin{array}{c}\mu =-5\\ k=5\end{array}$