SOLUTION: A(7,-2) and c (-1,-6) are the vertics of square abcd. Find the equations of diagonal ac and bd ?

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Question 987573: A(7,-2) and c (-1,-6) are the vertics of square abcd. Find the equations of diagonal ac and bd ?
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
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Find the slope of AC:
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m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29=%28-6-%28-2%29%29%2F%28-1-7%29=%28-4%29%2F%28-8%29=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=(%28x%5B1%5D%2Bx%5B2%5D%29%2F2,%28y%5B1%5D%2By%5B2%5D%29%2F2)
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Midpoint=(%287%2B%28-1%29%29%2F2,%28-2%2B-6%29%2F2
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Midpoint=(6%2F2,-8%2F2)=(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