How do you prove that the diagonals of a rectangle are equal in where the vertices are A(-6,5), B(12,-1), C(8,-13), and D(-10,-7)
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AC=√[(-6-8)^2+{5-(-13)}^2]
=√[(-14)^2+(5+13)^2]
=√[(-14)^2+(18)^2]
=√[196+324]
=√520
BD=√[{12-(-10)}^2+{(-1-(-7)}^2]
=√[(12+10)^2+(-1+7)^2]
=√[(22)^2+(6)^2)]
=√[484+36]
=√520
hence AC=BD
=√[(-14)^2+(5+13)^2]
=√[(-14)^2+(18)^2]
=√[196+324]
=√520
BD=√[{12-(-10)}^2+{(-1-(-7)}^2]
=√[(12+10)^2+(-1+7)^2]
=√[(22)^2+(6)^2)]
=√[484+36]
=√520
hence AC=BD
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