Question

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

Answer 1

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`