SOLUTION: Write an equation in standard form of the line that is the perpendicular bisector of the line segment with the given endpoints. (-2, 1) (8, 3)

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Question 117175: Write an equation in standard form of the line that is the perpendicular bisector of the line segment with the given endpoints.
(-2, 1) (8, 3)
Answer by checkley71(8403) (Show Source):
You can put this solution on YOUR website!
I REALLY MESSED UP ON THIS ON i WAS NOT THINKING STRAIGHT.
BELOW IS THE CORRECTD GRAPH.
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FIRST YOU NEED TO FIND THE SLOPE(m).
(3-1)/(8+2)=2/10=.2.
NOW YOU USE ONE SET OF POINTS & THE SLOPE TO SOLVE THE LINE EQUATION FOR THE Y INTERCEPT(b).
1=.2*3+b
1=.6+b
b=1-.6
b=.4
SO THIS LINE EQUATION IS:
Y=.2X+.4 (RED LINE)
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SO A PERPENDICULAR LINE WILL HAVE A SLOPE (m)=-5.
NOW YOU NEED TO FIND THE MID POINT BETWEEN THESE 2 POINTS.
Y DISTANCE=3-1=2 SO THE MID POINT IS 2/2=1 FROM EITHER END OR 3-1=2 OR [Y=2]
X DISTANCE=8-2=6 SO THE MID POINT IS 6/2=3 FROM EITHER END OR 8-3=5 OR [X=5]
(5,2) IS THE MID POINT WITH A SLOPE OF -5.
NOW YOU NEED TO SOLVE FOR THE Y INTERCEPT(b)
2=-5*5+b
2=-25+b
b=27
SO THIS PERPENDICULAR LINE EQUATION IS:
Y=-5X+27 (GREEN LINE)
(graph 300x300 pixels, x from -6 to 25, y from -6 to 25, of TWO functions y = .2x +.4 and y = -5x +27).