How do I find the equation of the perpendicular bisector of the line segment whose endpoints are (-4, 8) and (-6, -2) using the Midpoint Formula?

1 Answer
mason m
Nov 14, 2015

#y=-1/5x+2#

Explanation:

First, you must find the midpoint of the segment, the formula for which is #((x_1+x_2)/2,(y_1+y_2)/2)#. This gives #(-5, 3)# as the midpoint. This is the point at which the segment will be bisected.

Next, since we are finding a perpendicular bisector, we must determine what slope is perpendicular to that of the existing segment. To determine the segment's slope, we use the slope formula #(y_2-y_1)/(x_2-x_1)#, which gives us a slope of #5#.

Perpendicular lines have opposite and reciprocal slopes. The opposite reciprocal of #5# is #-1/5#.

We now know that the perpendicular travels through the point #(-5,3)# and has a slope of #-1/5#.

Solve for the unknown #b# in #y=mx+b#.

#3=-1/5(-5)+b=>3=1+b=>2=b#

Therefore, the equation of the perpendicular bisector is #color(blue)(y=-1/5x+2)#.

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