Show that the following points are the vertices of a rectangle:
A(2, – 2), B(14, 10), C(11, 13) and D(– 1, 1)
AB = √{(14 – 2)2 + (10 – (– 2))2}
= √{144 + 144} = √288
BC = √{(11 – 14)2 + (10 – 13)2}
= √{9 + 9} = √18 units
CD = √{(– 1 – 11)2 + (1 – 13)2}
= √{144 + 144}
= √288 units
DA = √{(– 1 – 2)2 + (1 – (– 2))2}
= √{9 + 9} = √18units
AB = CD and BC = DA
AC = √{(11 – 2)2 + (13 – (– 2))2}
= √{81 + 225}
= √306 units
For a Rectangle
AC2 = AB2 + BC2
Here AC2 = 306
But AB2 + BC2 = 288 + 18 = 306
∴ ABCD is a rectangle
32