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


`( (-1 -7)/(2) , (-3 -1)/(2) ) = (-4, -2)` <-- midpoint of mn

next you find the slope of mn which is


`(-3 -1)/(-1 -7) = (-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))