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

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05 Sep 2011, 01:16

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A

B

C

D

E

Difficulty:

75% (hard)

Question Stats:

51% (01:39) correct 49% (01:12) wrong based on 429 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)

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

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

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, 01:34

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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 8611 times ]

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

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31 Aug 2012, 02:26

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

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

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31 Aug 2012, 10:04

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.

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

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01 Sep 2012, 04:51

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, 16:16

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....

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

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29 Dec 2013, 13:50

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

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20 Jun 2014, 13:01

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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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