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Question 579216: Find a general form of an equation for the perpendicular bisector of the segment AB.A(8,4)B(-4,14)
Answer by mananth(16946)   (Show Source):
You can put this solution on YOUR website! .A(8,4)B(-4,14)
First find the midpoint co ordinates (x,y)
x= (x1+x2)/2
y=(y1+y2)/2
x=(8-4)/2 = 2
y= (14+4)/2 = 9
The perpendicular bisector passes through (2,9)
Find the slope of the line, A(8,4)B(-4,14)
x1 y1 x2 y2
8 4 -4 14
slope m = (y2-y1)/(x2-x1)
(14-4)/(-4-8)
( 10 / -12 )
m= - 5/ 6
the line perpendicular to this line will have a slope of (6/5) ( negative reciprocal)
The slope of the perpendicular line is (6/5) and it passes through (2,9)
m= 6/ 5
Plug value of the slope and point( 2 , 9 ) in
y=mx+b
9.00 = 6/5 * 2 +b
b= 9-12/5
b= 33/ 5
So the equation will be
Y = 6/5 x + 33/5
m.ananth@hotmail.ca
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