Question

Hello, i am terribly stuck on this question could someone please help me.I know these two point on a line, they are (2a,2c) and (2b,0) it asks me then to find the equation of the perpendicular bisector of this line. Ive spent 40 minutes on it and i havent gotten anywhere. Ive got up to the slop of the perpendicuar bisector and 1 point (the midpoint of AB (the line between coordinates)) Thanks to any help i can get

Answer 1

find the mindpoint.

then find the slope through the two points. slope = m
slope of the perpendicular is -1/m, where m is the slope through the two points.

use point slope form to get the equation of the perpendicular bisector.

Answer 2

First get slope of line:
slope = 2c/(2a-2b) = c/(a-b)

Next get midpoint because "bisector" means the line will have to intersect at midpoint
midpoint = ((2a+2b)/2 , 2c/2 ) = (a+b , c)

slope of perpendicular line is opposite reciprocal of original slope
--> -(a+b)/c

next get the equation of line using above slope and the midpoint
y-c = -(a+b)/c (x -(a+b))

y = -(a+b)/c x + (a^2-b^2)/c + c

y = -(a+b)/c x + (a^2 -b^2 +c^2)/c

Answer 3

im sorry theres a typo, perpendicular slope should be -(a-b)/c

Answer 4

THANK YOU SOOOOOOOOOO MUCH!! saved my evening

Answer 5

haha your welcome