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