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Write an equation of the perpendicular bisector of the segment with endpoints M(1,5) and N(7,−1).

 Mar 17, 2021
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The perpendicular bisector of a line segment goes through the midpoint and has slope which is the negative reciprocal of the slope of the line segment.

 

So, a point on the perpendicular bisector is ((1+7)/2, (5-1)/2) = (4, 2)

Slope of MN = (-1-5) / (7-1) = -6/6 = -1

Slope of perpendicular bisector = -1(1/(-1)) = 1

 

Equation of perpendicular bisector: y - 2 = 1(x - 4)

 

y = x - 2

 Mar 17, 2021

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