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In the rectangular coordinate system shown, ABCD is a quadrilateral. T

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In the rectangular coordinate system shown, ABCD is a quadrilateral. T [#permalink]

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New post 06 May 2017, 12:10
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  45% (medium)

Question Stats:

63% (00:57) correct 37% (02:05) wrong based on 30 sessions

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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

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Re: In the rectangular coordinate system shown, ABCD is a quadrilateral. T [#permalink]

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New post 06 May 2017, 12:25
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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
Re: In the rectangular coordinate system shown, ABCD is a quadrilateral. T   [#permalink] 06 May 2017, 12:25
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In the rectangular coordinate system shown, ABCD is a quadrilateral. T

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