SajjadAhmad wrote:
Source: Nova GMAT
In the rectangular coordinate system shown, ABCD is a quadrilateral. The coordinates of the points A , B , C, and D are (0, 2), (a, b), (a, 2), and (0, 0), respectively. Is the quadrilateral ABCD a parallelogram?
(1) a = 3
(2) b = 5
For a parallelogram, opposite sides are parallel and equal.
Statement 1: we get the x co-ordinates of point B & C but as we know nothing about point's B y co-ordinate "b", hence we cannot calculate the lengths of AB & BC. hence not sufficient
Statement 2: this gives us y co-ordinate of point B. So BC = 5-2 = 3 units whereas AD = 2-0 = 2 units. Clearly BC is not equal to its opposite side AD. hence it is not a parallelogram. Sufficient.
Hence option
B