Question

Write an equation in point-slope form for the perpendicular bisector of the segment with endpoints m(-1,-3) and n(7,1)

Answer 1

To find the perpendicular bisector, you have to find the midpoint of mn
which is

$( \frac{-1 -7}{2} , \frac{-3 -1}{2} ) = (-4, -2)$  <-- midpoint of mn

next you find the slope of mn which is
 
$\frac{-3 -1}{-1 -7} = \frac{-4}{-8} = 1/2$ <- this is the slope

to find the perpendicular slope, you take the negative recipricol which is

-2

so now we know the perpendicular bisector line has a slope of -2 and passes through (-4, -2)

so 

y-(-2) = -2(x-(-4))