How do you find the equation that is the perpendicular bisector of the line segment with endpoints #(-2, 4)# and #(6, 8)#?

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Answer 1 · 2016-07-22T13:07:26

Equation of the perpendicular bisector: #y = -2x+10#

First we need to find the slope of the line joining these points:

#m = (y_2-y_1)/(x_2-x_1) = (8-4)/(6-(-2)) = 4/8 = 1/2#

The line perpendicular to this will have #m = -2#

We also need the co-ordinates of the midpoint.

#M((x_1+x_2)/2 ; (y_1+y_2)/2)#

#M((-2+6)/2 ; (4+8)/2)#

#M(2,6)#

Use the formula for slope and one point:
#y-y_1 = m(x-x_1)#

#y -6 = -2(x-2)#

#y = -2x+4+6#

Equation of the perpendicular bisector: #y = -2x+10#