Expert: Azeem Hussain - 6/29/2009

Question
It has been a LONG time since I did Geometry.  Can you help me understand this?  Do I draw this or is there a math way to figure this out???

Point A located at (8,4) and point B located at (-2, -2). Please find the equation of a line that is the PERPENDICULAR BISECTOR of the line AB.  

Answer
Hi Susan!

There is a mathematical way of figuring this out.  Begin by finding the slope of AB.  This is done by dividing the change in y by the change in x ("rise over run").  Let the slope of AB equal m_AB.
m_AB=(-2-4)/(-2-8)
m_AB=-6/-10
m_AB=3/5

Perpendicular lines have slopes that are negative reciprocals of each other.  This means you flip the fraction and throw a negative sign in front of it.  Let's call the perpendicular bisector NM, so you're solving for m_NM.
m_NM=-(m_AB)^-1
m_NM=-(3/5)^-1
m_NM=-5/3

You have the slope, now you need to find the intercept b for the equation y=mx+b.  The questions asks for a perpendicular BISECTOR, which means you need the midpoint of AB, point M.  this is done by taking the average x-value and the average y-value.
M:((8-2)/2 , (4-2)/2)
M:(6/2 , 2/2)
M:(3,1)

Plug these coordinates and the slope of MN into the slope-intercept formula to solve for b.
y=mx+b
(1)=(-5/3)(3)+b
1=-5+b
b=6

ANSWER: The equation of the perpendicular bisector is y=-5x/3+6