Question 1015740
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For the segment:
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{{{P[1]}}}=({{{x[1]}}},{{{y[1]}}})=(1,2)
{{{P[2]}}}=({{{x[2]}}},{{{y[2]}}})=(-5,12)
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Slope=m={{{(y[2]-y[1])/(x[2]-x[1])}}}={{{(12-2)/(-5-1)=-10/6}}}=-5/3
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midpoint=({{{(x[1]+x[2])/2}}},{{{(y[1]+y[2])/2}}})
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midpoint=({{{(1+(-5))/2}}},{{{(2+12)/2}}})
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midpoint=({{{-4/2}}},{{{14/2}}})
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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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