Question 987573
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Find the slope of AC:
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{{{m=(y[2]-y[1])/(x[2]-x[1])}}}={{{(-6-(-2))/(-1-7)=(-4)/(-8)}}}={{{0.5}}}
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Using slope-intercept form:
y=mx+b
y=0.5x+b Put in values from one of the points and solve for b.
-2=(0.5)7+b
-2=3.5+b
-5.5=b Put this value in for b.
y=0.5x-5.5 This is the equation for diagonal AC.
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The diagonal BD will have the negative reciprocal of the slope of diagonal AC for its slope, and will pass through the midpoint of segment AC.
Slope: m=-2
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Midpoint=({{{(x[1]+x[2])/2}}},{{{(y[1]+y[2])/2}}})
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Midpoint=({{{(7+(-1))/2}}},{{{(-2+-6)/2}}}
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Midpoint=({{{6/2}}},{{{-8/2}}})=({{{3}}},{{{-4}}})
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Using slope-intercept form:
y=mx+b
y=-2x+b Put in midpoint values and solve for b.
-4=(-2)(3)+b
-4=-6+b
2=b 
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y=-2x+2 This is the equation of diagonal BD