Show that the points A(2, 1), B(5, 2), C(6, 4) and D(3, 3) are the angular points of a parallelogram. Is this figure a rectangle?


AB = √{(5 – 2)2 + (2 – 1)2} = √{9 + 1} = √10 units


BC = √{(6 – 5)2 + (4 – 2)2} = √{1 + 4} = √5 units


CD = √{(3 – 6)2 + (3 – 4)2} = √{9 + 1} = √10 units


DA = √{(3 – 2)2 + (3 – 1)2} = √{1 + 4} = √5 units


Since AB = CD and BC = DA


ABCD is Parallelogram


AC = √{(6 – 2)2 + (4 – 1)2} = √{16 + 9} = 5 units


For a Rectangle


AC2 = AB2 + BC2


Here AC2 = 25


But AB2 + BC2 = 15


ABCD is not a rectangle


30