Let and be the ends of a segment, then the slope of the line joining and is

The midpoint of the segment

can be finding as

The slope

of any perpendicular to the segment

is

Equation of perpendicular bisector of the segment

, being the equation of line through

and perpendicular to

using slope-point form is

Example: Find the equation of perpendicular bisector of and .

Equation of perpendicular bisector of is

Putting all these values in the equation we have

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