Question 1052356: Find the equation of the line perpendicular bisector of the line segment joining: (-3,8) and (5,-6)
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! The line joining (-3,8) and (5,-6) has slope of (-6-8)/(5-(-3))=-14/8=-7/4.
The line perpendicular to that has slope (4/7)
The midpoint of the first line is the average of -3 and 5 for x (which is 1) and 8 and -6 for y (or 1). The midpoint is (1,1)
We now have the slope and one point for the perpendicular bisector, and with the point-slope formula, y-y1=m(x-x1), where m is the slope and (x1,y1) a point,
y-1=(4/7)(x-1)
That is y=(4/7)x-(4/7)+1, or y=(4/7)x+(3/7).
The original line has an equation, again by the point slope formula,
of y-(-6)=(-7/4)(x-5)
That is y+6=-(7/4)x+(35/4). 6=24/4
so y=-(7/4)x+(11/4)
 The perpendicular bisector has the positive slope and the original line has a negative slope.
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