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In the xy-plane, the coordinates of two vertexes of parallelogram are

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houston1980
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In the xy-plane, the coordinates of two vertexes of parallelogram are [#permalink] New post   Updated on: 13 Jun 2021, 02:26
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In the xy-plane, the coordinates of two vertexes of parallelogram are (3,8) and (3,12) . What are the co-ordinates of the forth vertex?

1. The coordinates of the third vertex are (6,9)
2. The coordinates of the forth vertex are positive.
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E

Originally posted by houston1980 on 12 Jun 2021, 21:13.
Last edited by Bunuel on 13 Jun 2021, 02:26, edited 1 time in total.
Renamed the topic.
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harshtandel838
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Re: In the xy-plane, the coordinates of two vertexes of parallelogram are [#permalink] New post   12 Jun 2021, 21:25
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We know that..... The opposite sides of a parallelogram are equal in length, and the opposite angles are equal in measure.

From question, we know one side of parallelogram. If we know value of any other point we are able to draw whole shape!

So, Statement 1 is sufficient

But, statement 2 is not
Hence, answer is A

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Makesh89
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Re: In the xy-plane, the coordinates of two vertexes of parallelogram are [#permalink] New post   12 Jun 2021, 23:03
Statement A. Is NS reason the forth vertex can be above 6,9 or below or even negative.
Statement B. Tells us that they can be positive leaving us with two possibilities. Therefore NS Combined. No new information
Therefore E.

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In the xy-plane, the coordinates of two vertexes of parallelogram are [#permalink] New post   13 Jun 2021, 12:44
houston1980 wrote:
In the xy-plane, the coordinates of two vertexes of parallelogram are (3,8) and (3,12) . What are the co-ordinates of the forth vertex?

1. The coordinates of the third vertex are (6,9)
2. The coordinates of the forth vertex are positive.


The forth vertex coordinates can be (6,13) or (6,5).

Therefore the answer is E. Statement 1 and Statement 2 are NOT sufficient.
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Re: In the xy-plane, the coordinates of two vertexes of parallelogram are [#permalink] New post   18 Jul 2021, 22:31
The key to solving the problem is to distinguish cleraly between a square, a rectangle and a parallelogram
state 1 :

The coordinates of the fourth point can be can be (6,13) or (6,5).
depending on whether it was closer to (3,8) and (3,12) respectively
insuff
state 2 :
The coordinates of the forth vertex are positive
highly insuff
even combined we are not able to arrive at a correct conclusion
Hence IMO E
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Re: In the xy-plane, the coordinates of two vertexes of parallelogram are [#permalink]
18 Jul 2021, 22:31
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Bunuel
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