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In the x-y plane,the coordinates of three consecutive vertices of a

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In the x-y plane,the coordinates of three consecutive vertices of a [#permalink]

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New post 30 Jul 2017, 08:44
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In the x-y plane,the coordinates of three consecutive vertices of a rectangle are (2a,b),(-2a,b),(-2a,-3b).If a and b are integers with a<0 and b>0.Which of the following could be the coordinates of the fourth vertex?

A. (-3,-2)
B. (-2,3)
C. (6,-9)
D. (-6,-9)
E. (-6,9)
[Reveal] Spoiler: OA

Last edited by DHAR on 30 Jul 2017, 19:02, edited 3 times in total.

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Re: In the x-y plane,the coordinates of three consecutive vertices of a [#permalink]

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New post 30 Jul 2017, 10:13
DH99 wrote:
In the x-y plane,the coordinates of three consecutive vertices of a rectangle are (2a,b),(-2a,b),(-2a,-3b).If a and b are integers with a<0 and b>0.Which of the following could be the coordinates of the fourth vertex?

A. (-3,-2)
B. (-2,-3)
C. (6,-9))
D. (-6,-9)
E. (-6,9)

DH99 , both B and D are possible.

For B, a = -1, b = 1
(-2,1), (2,1), (2,-3), and (-2,-3) for the coordinate (2a, -3b)(a square is a rectangle)

For D, a = -3, b = 3

Are the answer choices correct? Or am I missing something really obvious? Maybe b is supposed to be >1?
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Last edited by generis on 30 Jul 2017, 10:17, edited 1 time in total.

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Re: In the x-y plane,the coordinates of three consecutive vertices of a [#permalink]

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New post 30 Jul 2017, 10:17
DH99 wrote:
In the x-y plane,the coordinates of three consecutive vertices of a rectangle are (2a,b),(-2a,b),(-2a,-3b).If a and b are integers with a<0 and b>0.Which of the following could be the coordinates of the fourth vertex?

A. (-3,-2)
B. (-2,-3)
C. (6,-9))
D. (-6,-9)
E. (-6,9)


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Re: In the x-y plane,the coordinates of three consecutive vertices of a [#permalink]

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New post 30 Jul 2017, 10:36
genxer123 wrote:
DH99 wrote:
In the x-y plane,the coordinates of three consecutive vertices of a rectangle are (2a,b),(-2a,b),(-2a,-3b).If a and b are integers with a<0 and b>0.Which of the following could be the coordinates of the fourth vertex?

A. (-3,-2)
B. (-2,-3)
C. (6,-9))
D. (-6,-9)
E. (-6,9)

DH99 , both B and D are possible.

For B, a = -1, b = 1
(-2,1), (2,1), (2,-3), and (-2,-3) for the coordinate (2a, -3b)(a square is a rectangle)

For D, a = -3, b = 3

Are the answer choices correct? Or am I missing something really obvious? Maybe b is supposed to be >1?


I share the same doubt.

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In the x-y plane,the coordinates of three consecutive vertices of a [#permalink]

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New post 31 Jul 2017, 17:35
Mo2men wrote:
genxer123 wrote:
DH99 wrote:
In the x-y plane,the coordinates of three consecutive vertices of a rectangle are (2a,b),(-2a,b),(-2a,-3b).If a and b are integers with a<0 and b>0.Which of the following could be the coordinates of the fourth vertex?

A. (-3,-2)
B. (-2,-3)
C. (6,-9))
D. (-6,-9)
E. (-6,9)

DH99 , both B and D are possible.

For B, a = -1, b = 1
(-2,1), (2,1), (2,-3), and (-2,-3) for the coordinate (2a, -3b)(a square is a rectangle)

For D, a = -3, b = 3

Are the answer choices correct? Or am I missing something really obvious? Maybe b is supposed to be >1?


I share the same doubt.

DH99 , I appreciate your effort in posting the question. When you correct a question, as I see you have done here by changing Answer B, would you please post that you have done so?

To post a correction is customary, in part because we who asked about accuracy get notified that you have answered. When you edit, we do not get such a notification. Thanks.
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Re: In the x-y plane,the coordinates of three consecutive vertices of a [#permalink]

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New post 08 Dec 2017, 05:29
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Plot the points on paper with axes, you'll see that the fourth vertex is (2a,-3b).
According to the question, a<0, so 2*a would be a negative number.
And b>0, so -3*b would also be a negative number.

With that in mind, only 2 answer choices fit the bill, A and D.
Again, it's mentioned that a is an integer, so 2*a would never be (-3) as stated in Option A. Thus, our answer is Option D.
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Kudos [?]: 6 [1], given: 49

Re: In the x-y plane,the coordinates of three consecutive vertices of a   [#permalink] 08 Dec 2017, 05:29
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