Write an equation of the perpendicular bisector of the segment with end points m(1,5) and n(7,-1)

The perpendicular bisector of the segment passes through the midpoint of this segment. Thus, we will initially find the midpoint P:



Now, we will calculate the slope of the segment support line (r). After this, we will use the fact that the perpendicular bisector (p) is perpendicular to r:





We can calculate the equation of p by using its slope and its point P: