ABCD is a parallelogram on xy rectangular coordinate plane

Question

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)

SOURH7WK · Accepted Answer

The answer is option E. For better clarity please refer the picture attached. (Green Lines represents the correct answer).

denver2018 · Answer

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

hiimmunish · Answer

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

chawlavinu · Answer

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??

hiimmunish · Answer

Other than (15,25), none is an option.

Spidy001 · Answer

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.

bindiyajoisher · Answer

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

fluke · Answer

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.

catfreak · Answer

Yup there are precisely 3 possible points 
a) -5,25 
b) -5,5
c) 15,25 which is the answer. 
Hence E.

chawlavinu · Answer

Fluke,

I am still consfused for you choosing the third option (15,25). Why didn't you choose the other two possible options?

thevenus · Answer

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

ratinarace · Answer

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

Zinsch123 · Answer

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.

dexerash · Answer

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.

Archit143 · Answer

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......

felixjkz · Answer

Well, I still see 3!!! parallelograms.
Why is square not a parallelogram?

gauravsoni · 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.

PiyushK · Answer

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.

sisirkant · Answer

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.

ABCD is a parallelogram on xy rectangular coordinate plane

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GMAT Problem Solving (PS) Questions

ABCD is a parallelogram on xy rectangular coordinate plane

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