Show that the following points are the vertices of a rectangle:
A(0, – 4), B(6, 2), C(3, 5) and D(– 3, – 1)
AB = √{(6 – 0)2 + (2 – (– 4))2}
= √{36 + 36}
= √72units
BC = √{(3 – 6)2 + (5 – 2)2}
= √{9 + 9}
= √18units
CD = √{(3 – (– 3))2 + (– 1 – 5)2}
= √{36 + 36}
= √72 units
DA = √{(– 3 – 0)2 + (– 1 – (– 4))2}
= √{9 + 9}
= √18units
AB = CD and BC = DA
AC = √{(3 – 0)2 + (5 – (– 4))2}
= √{9 + 81}
= √90 units
For a Rectangle
AC2 = AB2 + BC2
Here AC2 = 90
But AB2 + BC2 = 72 + 18 = 90
∴ ABCD is a rectangle
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