Question

Find the equation of a line which is equidistant from the lines x = - 2 and x = 6.

Answer 1

$\text{Let x =}\lambda \text{be the line equidistant from}x=-2andx=6so\left|\frac{-2-\lambda }{\sqrt{1}}\right|=\left|\frac{\lambda -6}{\sqrt{1}}\right|-2-\lambda =\lambda -6-2+6=\lambda +\lambda 4=2\lambda \therefore \lambda =2\therefore \text{The line equidistant from x = - 2 and x = 6 is x = 2}$