SOLUTION: The "perpendicular bisector" of the line segment line AB is the line that passes through the midpoint of line AB and is perpendicular to line AB. The equation of the perpendicul

Algebra ->  Points-lines-and-rays -> SOLUTION: The "perpendicular bisector" of the line segment line AB is the line that passes through the midpoint of line AB and is perpendicular to line AB. The equation of the perpendicul      Log On


   

Question 1015740: The "perpendicular bisector" of the line segment line AB is the line that passes through the midpoint of line AB and is perpendicular to line AB.
The equation of the perpendicular bisector of the line segment joining the points (1,2) and (-5,12) is y = mx + b. Find m+b.
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
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For the segment:
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P%5B1%5D=(x%5B1%5D,y%5B1%5D)=(1,2)
P%5B2%5D=(x%5B2%5D,y%5B2%5D)=(-5,12)
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Slope=m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29=%2812-2%29%2F%28-5-1%29=-10%2F6=-5/3
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midpoint=(%28x%5B1%5D%2Bx%5B2%5D%29%2F2,%28y%5B1%5D%2By%5B2%5D%29%2F2)
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midpoint=(%281%2B%28-5%29%29%2F2,%282%2B12%29%2F2)
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midpoint=(-4%2F2,14%2F2)
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midpoint=(-2,7)
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For perpendicular bisector:
slope=m=3/5 (negative reciprocal of slope of original segment)
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To find b, replace x and y with midpoint values:
x=-2; y=7
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y=3/5x+b
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7=(3/5)(-2)+b
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7=(-6/5)+b
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35/5+6/5=b
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41/5=b
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ANSWER: m=3/5; b=41/5
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