Jul 23 10:00 PM PDT  11:00 PM PDT This period of time is long enough: it gives you more than enough time to comfortably learn, review and practice all of the material. On the other hand it is not too long. Jul 24 11:30 PM EDT  10:00 PM EDT Free GRE Class: First Session. Experience the power of live instruction, for free. Our sample classes showcase our passionate and dedicated faculty and the way they'll guide you through proven strategies for improving your score. Jul 25 07:00 PM EDT  08:00 PM EDT Strategies and techniques for approaching featured GRE topics. An introduction to one of Manhattan Prep’s GRE worldclass instructors. Jul 29 10:00 PM PDT  11:00 PM PDT A Revolutionary OnDemand GRE Prep Course. Try for $1 Jul 30 10:00 PM PDT  11:00 PM PDT 7+ POINT GRE SCORE IMPROVEMENT GUARANTEE Jul 31 10:00 PM PDT  11:00 PM PDT Sign up for 1 Week GRE Prep
Author 
Message 
TAGS:


Manager
Joined: 12 Jan 2016
Posts: 144
Followers: 1
Kudos [?]:
73
[1]
, given: 17

Parallelogram ABCD lies in the xy plane [#permalink]
22 Sep 2016, 10:14
1
This post received KUDOS
Question Stats:
50% (03:15) correct
50% (02:44) wrong based on 26 sessions
Attachment:
#GREpracticequestion Parallelogram ABCD lies in the xyplane, as shown in the figure above..jpg [ 23.49 KiB  Viewed 333 times ]
Parallelogram ABCD lies in the xyplane, as shown in the figure above. The coordinates of point C are (3, 4) and the coordinates of point B are (7, 7). What is the area of the parallelogram ? A. 1 B. \(2 \sqrt{7}\) C. 7 D. 8 E. \(7 \sqrt{2}\)
Last edited by Sonalika42 on 22 Sep 2016, 20:39, edited 1 time in total.




GRE Prep Club Legend
Joined: 07 Jun 2014
Posts: 4809
WE: Business Development (Energy and Utilities)
Followers: 123
Kudos [?]:
1975
[0], given: 397

Re: Parallelogram ABCD lies in the xy plane [#permalink]
22 Sep 2016, 11:44
Given that point A is(0,0) (from figure) and B (3, 4) and C (7, 7). Now we know that area of a triangle \(\frac{1}{2}(x1(y2y3)+x2(y3y1)+x3(y1y2))\) where we have (x1,y1), (x2, y2) and (x3, y3) as three vertices of the triangle. Area of the triangle=\(\frac{1}{2}(x1(y2y3)+x2(y3y1)+x3(y1y2))\) =\(\frac{1}{2}(0(4(7))3(70)7(0(4)))\) =\(\frac{1}{2}(3(7)7(4))\)=3.5 So from geometry we can say that area of parallelogram ABCD = 2* area of the triangle ABC = 2*3.5 =7. Hence option C is the right answer.
_________________
Sandy If you found this post useful, please let me know by pressing the Kudos Button
Try our free Online GRE Test



Manager
Joined: 12 Jan 2016
Posts: 144
Followers: 1
Kudos [?]:
73
[0], given: 17

Re: Parallelogram ABCD lies in the xy plane [#permalink]
22 Sep 2016, 20:39
Hi Sandy,
Thanks a lot for all your replies, it really helps a lot.



Founder
Joined: 18 Apr 2015
Posts: 7426
Followers: 126
Kudos [?]:
1457
[1]
, given: 6628

Parallelogram ABCD lies in the xyplane, as shown in [#permalink]
06 Aug 2017, 12:28
1
This post received KUDOS
Attachment:
#GREpracticequestion Parallelogram ABCD lies in the xyplane, as shown in the figure above..jpg [ 23.49 KiB  Viewed 859 times ]
Parallelogram ABCD lies in the xyplane, as shown in the figure above. The coordinates of point C are (3, 4) and the coordinates of point B are (7, 7). What is the area of the parallelogram ? A. 1 B. \(2 \sqrt{7}\) C. 7 D. 8 E. \(7 \sqrt{2}\)
_________________
Get the 2 FREE GREPrepclub Tests



Intern
Joined: 23 Mar 2017
Posts: 16
Followers: 0
Kudos [?]:
9
[1]
, given: 4

Re: Parallelogram ABCD lies in the xyplane, as shown in [#permalink]
09 Aug 2017, 23:18
1
This post received KUDOS
can u explain the solution?



Intern
Joined: 30 Aug 2017
Posts: 1
Concentration: Finance, Economics
WE: Investment Banking (Investment Banking)
Followers: 0
Kudos [?]:
1
[1]
, given: 0

Re: Parallelogram ABCD lies in the xyplane, as shown in [#permalink]
31 Aug 2017, 21:20
1
This post received KUDOS
The easiest way to solve this problem is to draw a rectangle around the parallelogram, find its area, and substract area of the triangles that emerge around the parallelogram, within the rectangle (but that are not part of the parallelogram). Since ABCD is a parallelogram, line segments AB and CD have the same length and the same slope. Therefore, in the diagram above, point A is at (4,3), The square has an area of 7*7=49. By drawing carefully and exploiting similar triangles created by various parallel lines, you can label the height of each triangle 3, and each base 7. Each triangles has area 1/2hb=1/2*3*7=21/2. Therefore, the area of the parallelogram ABCD equals 494*(21/2)=4942=7.



Intern
Joined: 20 Sep 2017
Posts: 15
WE: Analyst (Consulting)
Followers: 0
Kudos [?]:
7
[1]
, given: 11

Re: Parallelogram ABCD lies in the xyplane, as shown in [#permalink]
16 Jan 2018, 05:28
1
This post received KUDOS
First find the coordinates of point A. For now, lets assume the coordinates are (x,y) Since it is mentioned that ABCD is a parallelogram. So slope of BC must be equal to slope of AD since BCAD. Hence we can get the equation 3x=4y=0  equation(1) [by equating slope of line BC and AD]
Similarly by equating the lines AB and CD since (ABCD), we get the equation 4x+3y= 7  (2)
Solving for equations (1) and (2) we get x = 4 and y= 3. Thus A is (4,3).
If we observe now, all sides are equal in length i.e. each side AB=BC=CD=AD=5. Thus ABCD is a rhombus. The area of a rhombus is (product of lengths of diagonals)/2 i.e. in our case (BD*AC)/2.
BD is 7*(2)^(1/2) and AC is 2^(1/2). Thus area of ABCD is 7{sqrt2} * {sqrt2} = 7
option C



Intern
Joined: 12 Nov 2018
Posts: 25
Followers: 0
Kudos [?]:
8
[0], given: 17

Re: Parallelogram ABCD lies in the xy plane [#permalink]
05 Jun 2019, 07:32
can you please show in figure please for better understanding ? regards,




Re: Parallelogram ABCD lies in the xy plane
[#permalink]
05 Jun 2019, 07:32





