What is the perpendicular bisector of a line with points at A #(-33, 7.5)# and B #(4,17)#?

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Answer 1 · 2016-03-11T08:54:55

Equation of perpendicular bisector is #296x+76y+3361=0#

Let us use point slope form of equation, as the desired line passes through mid point of A #(-33,7.5)# and B#(4,17)#.

This is given by #((-33+4)/2,(7.5+17)/2)# or #(-29/2,49/4)#

The slope of line joining A #(-33,7.5)# and B#(4,17)# is #(17-7.5)/(4-(-33))# or #9.5/37# or #19/74#.

Hence slope of line perpendicular to this will be #-74/19#, (as product of slopes of two perpendicular lines is #-1#)

Hence perpendicular bisector will pass through #(-29/2,49/4)# and will have a slope of #-74/19#. Its equation will be

#y-49/4=-74/19(x+29/2)#. To simplify this multiply all by #76#, LCM of the denominators #2,4,19#. Then this equation becomes

#76y-49/4xx76=-74/19xx76(x+29/2)# or

#76y-931=-296x-4292# or #296x+76y+3361=0#