# Equation of the Right Bisector of a Triangle

To find the equation of the right bisector of a triangle we examine the following example: Consider the triangle having vertices $A\left( { - 3,2} \right)$, $B\left( {5,4} \right)$ and $C\left( {3, - 8} \right)$.

The equation of a perpendicular bisector is given as

For the perpendicular bisector of $A\left( { - 3,2} \right)$ and $B\left( {5,4} \right)$, and putting these values in the above equation (i), we have

This is the equation of the perpendicular bisector of $A\left( { - 3,2} \right)$ and $B\left( {5,4} \right)$

For the perpendicular bisector of $B\left( {5,4} \right)$ and $C\left( {3, - 8} \right)$, and putting these values in the above equation (i), we have

This is the equation of the perpendicular bisector of $B\left( {5,4} \right)$ and $C\left( {3, - 8} \right)$

For the perpendicular bisector of $C\left( {3, - 8} \right)$ and $A\left( { - 3,2} \right)$, and putting these values in the above equation (i), we have

This is the equation of the perpendicular bisector of $C\left( {3, - 8} \right)$ and $A\left( { - 3,2} \right)$.