Equation of the Right Bisector of a Line

Let $A\left( {{x_1},{y_1}} \right)$ and $B\left( {{x_2},{y_2}} \right)$ be the ends of a segment, then the slope ${m_1}$ of the line joining $A$ and $B$ is

The midpoint of the segment $AB$ can be found as

The slope $m$ of any line perpendicular to the segment $AB$ is

The equation of the perpendicular bisector of the segment$AB$ being the equation of a line through $C$ and perpendicular to $AB$ using the slope-point form is

Example: Find the equation of the perpendicular bisector of $A\left( {1,2} \right)$ and $B\left( {5, - 1} \right)$.

The equation of the perpendicular bisector of $AB$ is

Putting all these values in the equation, we have