Question 1038413
Slope of the given points:  {{{(1-(-5))/(4-2)=6/2=3}}}

Slope of any line perpendicular to line defined by the two given points,  {{{-1/3}}}.


Bisector of the SEGMENT of the two given points:
{{{system(x=(4+2)/2=3,y=(1-5)/2=-4/2=-2)}}}
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The point  (3,-2).



WANTED REQUESTED Perpendicular Bisector line:
{{{highlight(y+2=-(1/3)(x-3))}}}
which is in point-slope form.  You can change the form depending how you want it to be.