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A rectangle is plotted on the standard coordinate plane

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Re: A rectangle is plotted on the standard coordinate plane [#permalink] New post 15 Oct 2013, 04:36
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madn800 wrote:
Bunuel, I solved the problem using the concept of Pythagorean triplets.
Please check and tell if my solution is correct.
File attached below.


No, it's not correct. The answer is B, not D.

Check my post to see 2 possible scenarios for the first statement.
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Re: A rectangle is plotted on the standard coordinate plane [#permalink] New post 15 Oct 2013, 06:46
OK, got it.
Thanks. :-D
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Re: A rectangle is plotted on the standard coordinate plane [#permalink] New post 02 Jan 2014, 08:12
I think it should be c as 'non-negative integers' means it can be either negative non integer or positive integers. Please correct me if I'm wrong. Thanks!
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Re: A rectangle is plotted on the standard coordinate plane [#permalink] New post 03 Jan 2014, 03:46
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nariskat wrote:
I think it should be c as 'non-negative integers' means it can be either negative non integer or positive integers. Please correct me if I'm wrong. Thanks!


Non-negative integers mean integers more than or equal to zero: 0, 1, 2, ...

Hope it's clear.
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Re: A rectangle is plotted on the standard coordinate plane [#permalink] New post 01 Aug 2014, 15:15
B is sufficient. The distance from (0,0) to other vertices is 8. So can be point (0,8) or the distance can be the the diagonal length of 8. Then the other length of the rectangle will be \sqrt{( 8^2 -6^2)} = 2\sqrt{7}. And 2\sqrt{7} is not an integer, there is left with one choice. (0,8)
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Re: A rectangle is plotted on the standard coordinate plane [#permalink] New post 20 Dec 2014, 15:46
I think in either statement you have a distance that can be the x coordinate you need or the diagonal. With 10 you can have (10, 0) or a diagonal 10 in which case with the Pythagorean theorem the coordinates would be (8,0). This is possible so you don't now the solution.
If the distance is 8 you can have (8,0) or a diagonal that gives coordinates (square root of 28, 0) which is not an integer. So in this case the only possibility is for (8,0). Therefore Stat 2 is suf.
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Re: A rectangle is plotted on the standard coordinate plane [#permalink] New post 21 Dec 2014, 07:53
Bunuel can you explain why the rectangle can't be rotated a few degrees?
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Re: A rectangle is plotted on the standard coordinate plane [#permalink] New post 21 Dec 2014, 08:03
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bankerboy30 wrote:
Bunuel can you explain why the rectangle can't be rotated a few degrees?


Because we re told that the coordinates of all vertices of the rectangle are non-negative integers. If you rotate it this condition would be violated. I think the image here a-rectangle-is-plotted-on-the-standard-coordinate-plane-115697.html#p1098927 should help to visualize this.

Hope it helps.
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Re: A rectangle is plotted on the standard coordinate plane [#permalink] New post 17 May 2015, 07:56
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guygmat wrote:
A rectangle is plotted on the standard coordinate plane, with vertices at the origin and (0,6). If the coordinates of all vertices of the rectangle are non-negative integers, what are the coordinates of the other two vertices?

(1) The distance between the origin and one of the other vertices is 10 units.

(2) The distance between the origin and one of the other vertices is 8 units.


The question states that it is a rectangle, so if u look at statement 2.
8 units has to be the length along the x plain because for it to be a square a min length of 6*1.4 =8.4 is needed.
If the length is lower that 8.4, then rectangle would have lower part move into the 4th quadrant, hence 8 has to be along the x axis and not
the diagonal length.

and statement 1 is not sufficient as its is more than 8.4 and hence the rectangle can be formed if it is a the diagonal or the horizontal length.
Re: A rectangle is plotted on the standard coordinate plane   [#permalink] 17 May 2015, 07:56

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