Find the equation of the perpendicular bisector of the line joining the points `(1,3)` and `(-2,6)`.

Explanation

Let the perpendicular bisector `CD` of the line joining the points `A(1,3)` and `B(-2,6)` meets `AB` at `M`.

Slope of `AB m_(1)=(6-3)/(-2-1)=-1`
Slope of `CD m_(2)=-(1)/(m_(1))=-(1)/(-1)=1`
Co-ordinates of mid-point `M` of `AB=((1-2)/(2),(3+6)/(2))`
`=(-(1)/(2),(9)/(2))`
Now, equation of line `CD y-(9)/(2)=m_(2)(x+(1)/(2))`
`implies y-(9)/(2)=1(x+(1)/(2))`
`implies x-y+5=0`.