Write an equation of the perpendicular bisector of the segment with the endpoints (−3,4) and (5,8).

Answer 1

Bisector means cut in half: Find the midpoint: (-3+5)/2, (4+8)/2 = (1, 6)

Perpendicular means the slope is the opposite reciprocal. Find the slope: (8-4)/5--3 = 4/8=1/2

The perpendicular slope is -2

So now we have the slope and a point.

Plug in the point-slope equation: y-y1=m(x-x1)

y-6=-2(x-1)

Distribute the -2

y-6=-2x+2

solve for y by adding 6 to both sides

y= -2x+8