SOLUTION: Find the equation of the perpendicular bisector of the segment AB, if A(1, �2.5) and B(5, 5.5). If the perpendicular bisector of AB intercepts the y-axis at point P, what are the

Question 1124693: Find the equation of the perpendicular bisector of the segment AB, if A(1, �2.5) and B(5, 5.5). If the perpendicular bisector of AB intercepts the y-axis at point P, what are the lengths of PA and PB?

Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
A(1, -2.5) and B(5, 5.5)
by mid point formula
{(x,y) = (x1+x2)/2 , (y1+y2)/2)
(1+5)/2 , (-2.5+5.5)/2
mid point of AB (3,1.5)
Find the slope of AB
m = (y1-y2)/(x1-x2)
(-2.5-5.5)/(1-5)
=2
Find the equation of perpendicular to AB
The slope of perpendicular line will bw negative reciprocal of AB = -1/2
Equation of perpendicular line
slope = (-1/2) passing through (3.1.5)
equation
y-y1- m(x-x1)
y-1.5) = (-1/2) (x-3)
2y-3= -x+3
2y+x = 6
y= 3-(x/2) equation of perpendicular line to AB

The line intersects at (0,y)
Plug x=0
y=3
The intersection point on y axis M(0,3) & B
Distance From (0,3) to B, (5,5.5)
Use distance formula
OM = sqrt((5.5-3)^2+(5-0)^2)
= 5.9
Both distances are equal

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