Show that the following points are the vertices of a rectangle:

A(– 4, – 1), B(– 2, – 4), C(4, 0) and D(2, 3)


A(– 4, – 1), B(– 2, – 4), C(4, 0) and D(2, 3)


AB = √{(– 2 – (– 4))2 + (– 4 – (– 1))2}


= √{4 + 9} = √13units


BC = √{(4 – (– 2))2 + (0 – (– 4))2}


= √{36 + 16} = √52units


CD = √{(2 – 4)2 + (3 – 0)2}


= √{4 + 9} = √13 units


DA = √{(2 – (– 4))2 + (3 – (– 1))2}


= √{36 + 16} = √52units


AB = CD and BC = DA


AC = √{(4 – (– 4))2 + (0 – (– 1))2}


= √{64 + 1} = √65 units


For a Rectangle


AC2 = AB2 + BC2


Here AC2 = 65


But AB2 + BC2 = 13 + 52 = 65


ABCD is a rectangle


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