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# ABCD is a parallelogram on xy rectangular coordinate plane

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Manager
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ABCD is a parallelogram on xy rectangular coordinate plane  [#permalink]

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05 Sep 2011, 02:16
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12
00:00

Difficulty:

75% (hard)

Question Stats:

57% (02:17) correct 43% (02:06) wrong based on 432 sessions

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ABCD is a parallelogram on xy rectangular coordinate plane, three of the four vertices of parallelogram are (5,15) , (5,25) and (-5,15). Which can be the coordinate of fourth vertex?

A. (-5,-5)
B. (5,15)
C. (-5,-25)
D. (-5,10)
E. (15,25)
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Re: ABCD is a parallelogram on xy rectangular coordinate plane  [#permalink]

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31 Aug 2012, 02:34
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The answer is option E. For better clarity please refer the picture attached. (Green Lines represents the correct answer).
Attachments

XY Graph.JPG [ 72.1 KiB | Viewed 10895 times ]

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##### General Discussion
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09 Sep 2011, 06:18
the answer is (15, 25) E. It's sense that the answer is E. the shape is parallelogram send the last point to the far right
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15 Sep 2011, 05:56
DeeptiM wrote:
pls help me with the elimination method..

since it is a parallelogram, co-ordinates of 4th point can be (15,25), (-5,5), or (-5,25). Now check from options.
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16 Sep 2011, 02:47
1
hiimmunish wrote:
DeeptiM wrote:
pls help me with the elimination method..

since it is a parallelogram, co-ordinates of 4th point can be (15,25), (-5,5), or (-5,25). Now check from options.

The options (-5,25) is also possible condidate since this option will make a square (a type of parallelogram).

Finally, (-5,25), (-5,5) and (15,25) all look the possible options. How do you really eliminate??
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16 Sep 2011, 06:08
chawlavinu wrote:
hiimmunish wrote:
DeeptiM wrote:
pls help me with the elimination method..

since it is a parallelogram, co-ordinates of 4th point can be (15,25), (-5,5), or (-5,25). Now check from options.

The options (-5,25) is also possible condidate since this option will make a square (a type of parallelogram).

Finally, (-5,25), (-5,5) and (15,25) all look the possible options. How do you really eliminate??

Other than (15,25), none is an option.
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16 Sep 2011, 21:10
none of the given options are correct. Correct option should be (-5,25)

adjacent sides are equal in length and perpendicular to each other. Hence this is a square.
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16 Sep 2011, 22:16
I also got the answer as (-5,25) but the options does not have it
so we can use the midpoint method as well correct

Thanks
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16 Sep 2011, 22:50
1
DeeptiM wrote:
ABCD is a parallelogram on xy rectangular coordinate plane, three of the four vertices of parallelogram are (5,15) , (5,25) and (-5,15). Which can be the coordinate of fourth vertex?

(-5,-5)
(5,15)
(-5,-25)
(-5,10)
(15,25)

From stem,
A(-5, 15)
B(5, 15)
C(5, 25)

There are at least 3 possible point I can think of:
X(-5, 25): Parallelogram=Square=AXCB, where AX||CB, AX=CB, XC||AB, XC=AB
Y(-5, 5): Parallelogram=AYBC, where AY||BC, AY=BC, AC||YB, AC=YB
Z(15, 25): Parallelogram=ACZB, where AC||ZB, AC=ZB, CZ||AB, CZ=AB

Ans: "E"
*************************************************************

Draw these on number line/graph.
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18 Sep 2011, 00:19
Yup there are precisely 3 possible points
a) -5,25
b) -5,5
c) 15,25 which is the answer.
Hence E.
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22 Sep 2011, 19:13
fluke wrote:
DeeptiM wrote:
ABCD is a parallelogram on xy rectangular coordinate plane, three of the four vertices of parallelogram are (5,15) , (5,25) and (-5,15). Which can be the coordinate of fourth vertex?

(-5,-5)
(5,15)
(-5,-25)
(-5,10)
(15,25)

From stem,
A(-5, 15)
B(5, 15)
C(5, 25)

There are at least 3 possible point I can think of:
X(-5, 25): Parallelogram=Square=AXCB, where AX||CB, AX=CB, XC||AB, XC=AB
Y(-5, 5): Parallelogram=AYBC, where AY||BC, AY=BC, AC||YB, AC=YB
Z(15, 25): Parallelogram=ACZB, where AC||ZB, AC=ZB, CZ||AB, CZ=AB

Ans: "E"
*************************************************************

Draw these on number line/graph.

Fluke,

I am still consfused for you choosing the third option (15,25). Why didn't you choose the other two possible options?
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30 Aug 2012, 22:23
1
ABCD is a parallelogram on xy rectangular coordinate plane, three of the four vertices of parallelogram are (5,15) , (5,25) and (-5,15). Which can be the coordinate of fourth vertex?

Draw the given coordinates on the xy plane and figure out which one will "connect the dot "

(-5,-5) falling in 4th quadrant -incorrect
(5,15) same point as one of the point already the parallelogram -incorrect
(-5,-25) falling in 4th quadrant -incorrect
(-5,10) improper to draw a parallelogram -incorrect
(15,25) correct
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Re: ABCD is a parallelogram on xy rectangular coordinate plane  [#permalink]

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31 Aug 2012, 03:26
By plotting the points one can easily point out the fourth vertex as (15,25) making the opposite sides parallel and equal so the right choice should be E) But I found this a bit lengthy..Is there any other way out
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Re: ABCD is a parallelogram on xy rectangular coordinate plane  [#permalink]

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31 Aug 2012, 11:04
ratinarace wrote:
By plotting the points one can easily point out the fourth vertex as (15,25) making the opposite sides parallel and equal so the right choice should be E) But I found this a bit lengthy..Is there any other way out
Plotting it does not take long. It need not be exact.

If it takes you long, maybe you should practice it a little bit.

The/another other option is plotting it in your mind.
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Re: ABCD is a parallelogram on xy rectangular coordinate plane  [#permalink]

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01 Sep 2012, 05:51
Instead of following any rule/formula, this question is much easier if done by making a drawing on the paper.
Without visualizing, it is difficult to eliminate the options.
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Re: ABCD is a parallelogram on xy rectangular coordinate plane  [#permalink]

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11 Nov 2012, 17:16
I have got a very simple doubt i think none of the options mentioned are correct.

If we consider one of the base as A as (-5,15) B as (5,15) so the distance is 11 units not by distance formula just by observation, this distance should be equal to CD given C is (5,25) hence to keep the distance of CD 11 units the X co ordinate should be either -5 or 16 and not 15..

Pls correct me if i am wrong, yes just by quick observation (15 , 25 ) is the correct answer....

But if calculating this isnt......
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Re: ABCD is a parallelogram on xy rectangular coordinate plane  [#permalink]

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06 Dec 2012, 00:26
SOURH7WK wrote:
The answer is option E. For better clarity please refer the picture attached. (Green Lines represents the correct answer).

Well, I still see 3!!! parallelograms.
Why is square not a parallelogram?
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Re: ABCD is a parallelogram on xy rectangular coordinate plane  [#permalink]

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17 Jun 2014, 09:22
SOURH7WK wrote:
The answer is option E. For better clarity please refer the picture attached. (Green Lines represents the correct answer).

Ok.. i don't get it. All rectangles are parallelograms so with the point (-5,25) we are getting a rectangle. So why cant it be the right answer.
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Re: ABCD is a parallelogram on xy rectangular coordinate plane  [#permalink]

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20 Jun 2014, 14:01
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There is a direct formula to solve this question, ABCD is a parallelogram with consecutive vertices (X1,Y1), (X2,Y2),(X3,Y3) AND (X4,Y4)

Then Formula EQ:
X1+X3=X2+X4
Y1+Y3=Y2+Y4

if three vertices are known you can find out fourth. but important is to know what are consecutive and what are opposite vertices.
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Re: ABCD is a parallelogram on xy rectangular coordinate plane  [#permalink]

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04 Jun 2017, 12:02
Made a mistake in calculating the coordinate. Selected (-5, 10) which should be (-5, 5) but (-5, 5) is not there the choices. So (15,25) is the answer.
Re: ABCD is a parallelogram on xy rectangular coordinate plane   [#permalink] 04 Jun 2017, 12:02

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