Cartesian Equation for the perpendicular bisector of a line 
Find the Cartesian equation for the perpendicular bisector of the line joining A(2,3) and B(0,6)

How do I do this?
Thank you! 

Notice, the slope of the line joining the given points $(2, 3)$ & $(0, 6)$
$$=\frac{6-3}{0-2}=\frac{-3}{2}$$ Now, the slope of the perpendicular bisector $$=\frac{-1}{\text{Slope of line}\space AB}=\frac{-1}{\frac{-3}{2}}=\frac{2}{3}$$ Now, the perpendicular bisector will pass through the mid-point of the line joining points $(2, 3)$ & $(0, 6)$ i.e. $\left(\frac{2+0}{2}, \frac{3+6}{2}\right)\equiv\left(1, \frac{9}{2}\right)$ Hence, the cartesian equation of the perpendicular bisector having slope $\frac{2}{3}$ & passing through the point $\left(1, \frac{9}{2}\right)$ is given as $$y-\frac{9}{2}=\frac{2}{3}(x-1)$$ $$\implies 6y-27=4x-4$$ $$\implies \color{blue}{4x-6y+23=0}$$
