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geometry ds

by resilient » Wed Mar 05, 2008 3:54 pm
quadrilateral pqrs has pq parallel RS and QR parallel PS. What is area of PQRS?

1. the coordinates of point pq are (2,0) and coordinates of Point R (8,2).

2. Coordinates of point S are (6,0).

qa is c. I am convinced that A is solution..
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by xilef » Wed Mar 05, 2008 4:59 pm
In A you said point PQ, I'll assume you meant P.

I think you are assuming that quadrilateral has all right angles. Here you have a quadrilateral that is also a parallelogram. It can look something like the diagram below. And even knowing P and R, you still need Q or S.
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Re: geometry ds

by Stuart@KaplanGMAT » Wed Mar 05, 2008 5:24 pm
Enginpasa1 wrote:quadrilateral pqrs has pq parallel RS and QR parallel PS. What is area of PQRS?

1. the coordinates of point pq are (2,0) and coordinates of Point R (8,2).

2. Coordinates of point S are (6,0).

qa is c. I am convinced that A is solution..
Since PQRS has two parallel sides, we know that it's a parallelogram. The area of a parallelogram is base * height, so that's what we need to know.

(1) P is at (2,0) and R is at (8,2)

An infinite number of parallelograms can be drawn with just two points. We could have a rectangle with points Q (2,2) and S (8,0). We could also have a paralellogram with points Q (7,2) and S (3,0). Each of these shapes could have a different area: insufficient.

(2) S is at (6,0).

Well, if two points aren't enough, 1 point certainly isn't.

Together: with 3 of the points known, the 4th point becomes fixed (in this case it would be (4,2)): sufficient.
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by hemanth28 » Wed Mar 05, 2008 7:54 pm
Enginpasa1,

you are assuming that the quadrilateral is parallel to the x and y axis.Then only your answer is right.
However its not mentioned anywhere.
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