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write an equation of the perpendicular bisector of the line segment whose endpoints are (-1,1) and (7,-5)

User Cfbarbero
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Find midpoint of segment.
(-1,1), (7,-5)

x= (-1+7)/(2)=3,y= (1+(-5))/(2)=-2

Find slope of line which passes through (-1,1) and (7,-5).

m= (-5-1)/(7-(-1))= (-6)/(8)=- (3)/(4)

The slope of perpendicular line is negative reciprocal value of m.

m_(\perp)=- (1)/(m) =- (1)/(- (3)/(4) ) = (4)/(3)

Write quation of line which slope is
(4)/(3) and passes throug the point (3,-2).

m=(4)/(3),x_1=3,y_1=-2 \\y-y_1=m(x-x_1) \\ \\y-(-2)=(4)/(3)(x-3) \\ \\y+2=(4)/(3)x-(8)/(3) \\ \\3y+6=4x-8 \\4x-3y-14=0

User Tsells
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