Question

write an equation of the perpendicular bisector of the line of the segment with endpoints Q -2 ,0 and R 6,12.​

Answer 1

Given :   line segment with endpoints Q( -2 ,0) and R( 6,12)

To  Find :  equation of the perpendicular bisector of the line segment

Solution:

line segment with endpoints Q( -2 ,0) and R( 6,12)

mid point  = ( -2 + 6)/2 , (0 + 12)/2

=  ( 2 ,  6)

slope =  (12 - 0)/(6 - (-2)) = 12/8  = 3/2

Slope of perpendicular = - 2/3

perpendicular bisector  pa sses through (2 , 6)

Hence  equation of the perpendicular bisector  

y - 6  = (-2/3)(x - 2)

=> 3y - 18  = -2x + 4

=> 2x  + 3y = 22

2x  + 3y = 22 is equation of the perpendicular bisector  

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