Author 
Message 
TAGS:


Manager
Joined: 27 Feb 2017
Posts: 189
Followers: 1
Kudos [?]:
53
[0], given: 15

f the coordinates of point B are (3, 4) and [#permalink]
10 Sep 2018, 16:30
Question Stats:
75% (00:43) correct
25% (01:56) wrong based on 4 sessions
Attachment:
geometry single 002.JPG [ 13.06 KiB  Viewed 1468 times ]
If the coordinates of point B are (3, 4) and the coordinates of point C are (7, 7), what is the area of the parallelogram? A. 1 B. \(2 \sqrt{7}\) C. 7 D. 8 E. \(7 \sqrt{2}\) I do not understand how did they get C as the answer.
Last edited by Carcass on 07 Apr 2019, 01:03, edited 1 time in total.
Edited by Carcass




Director
Joined: 20 Apr 2016
Posts: 864
WE: Engineering (Energy and Utilities)
Followers: 11
Kudos [?]:
645
[0], given: 141

Re: Find the area of a parallelogram [#permalink]
11 Sep 2018, 05:56
kruttikaaggarwal wrote:
I do not understand how did they get C as the answer.
Who are they? Can you plz check if the signs of all the coordinates are correct, as all the values are in 2nd quadrant
_________________
If you found this post useful, please let me know by pressing the Kudos Button
Rules for Posting https://greprepclub.com/forum/rulesfor ... 1083.html



Intern
Joined: 15 Sep 2017
Posts: 34
Followers: 0
Kudos [?]:
15
[0], given: 2

Re: Find the area of a parallelogram [#permalink]
11 Sep 2018, 06:23
[quote="kruttikaaggarwal"]If the coordinates of point B are (3, 4) and the coordinates of point C are (7, 7), what is the area of the parallelogram? Attachment: geometry single 002.JPG A. 1 B. 2√7 C. 7 D. 8 E. 7√2 I do not understand how did they get C as the answer.[/quotes] Really is the figure true? it contradicts with points given. In gre graphically representation can be taken exactly as in figure unlike geometric figures



Manager
Joined: 27 Feb 2017
Posts: 189
Followers: 1
Kudos [?]:
53
[0], given: 15

Re: Find the area of a parallelogram [#permalink]
11 Sep 2018, 10:56
pranab01 wrote: kruttikaaggarwal wrote:
I do not understand how did they get C as the answer.
Who are they? Can you plz check if the signs of all the coordinates are correct, as all the values are in 2nd quadrant Hi guys, I did recheck the question and I actually copypasted it as is. It is from one of the GRE prep club Quants test. This is the explanation they gave and I find it bizzare: Area of parallelogram ABCD = 2×ABD The coordinates of the vertices of triangle ABD are A(0,0),B(−3,−4),C(−7,−7). If one of the vertices of a triangle is at the origin and other two being (a,b),(c,d), then the area of the triangle can be written as : Area = (ad−bc)/2 Applying this formula to the triangle ABD, we get the area as [(−3)∗(−7)−(−4)∗(−7)]/2=7/2 So, the area of the parallelogram is twice the area of triangle ABD or 7/2 ×2 or 7sq.units. The correct answerC



GRE Prep Club Legend
Joined: 07 Jun 2014
Posts: 4857
WE: Business Development (Energy and Utilities)
Followers: 111
Kudos [?]:
1854
[0], given: 397

Re: Find the area of a parallelogram [#permalink]
11 Sep 2018, 18:18
Hi Krutika, Could you please share the question number so that we can fix the graph. The are aof a triangle with coordinate A (\(A_x\),\(A_y\)), B (\(B_x\),\(B_y\)) and C (\(C_x\),\(C_y\)) can be written as: area=\(\mod{\frac{A_x(B_yC_y)+B_x(C_yA_y)+C_x(A_yB_y)}{2}}\). Here one of the coordinates is (0,0). Thus the reduced expression in the explanation. Here is great tool to vizualize the same. https://www.mathopenref.com/coordtrianglearea.html
_________________
Sandy If you found this post useful, please let me know by pressing the Kudos Button
Try our free Online GRE Test



Director
Joined: 20 Apr 2016
Posts: 864
WE: Engineering (Energy and Utilities)
Followers: 11
Kudos [?]:
645
[0], given: 141

Re: Find the area of a parallelogram [#permalink]
11 Sep 2018, 22:09
sandy wrote: The are aof a triangle with coordinate A (\(A_x\),\(A_y\)), B (\(B_x\),\(B_y\)) and C (\(C_x\),\(C_y\)) can be written as:
area=\(\mod{\frac{A_x(B_yC_y)+B_x(C_yA_y)+C_x(A_yB_y)}{2}}\).
Hi Sandy, Can we accept in GRE the sign of the coordintes donot matter, As point c (7,7) and point B (3, 4). both of these lies in II quadrant as such both y coordinates should be positive. Can you plz enlighten me
_________________
If you found this post useful, please let me know by pressing the Kudos Button
Rules for Posting https://greprepclub.com/forum/rulesfor ... 1083.html



Manager
Joined: 27 Feb 2017
Posts: 189
Followers: 1
Kudos [?]:
53
[0], given: 15

Re: Find the area of a parallelogram [#permalink]
12 Sep 2018, 05:20
sandy wrote: Hi Krutika, Could you please share the question number so that we can fix the graph. The are aof a triangle with coordinate A (\(A_x\),\(A_y\)), B (\(B_x\),\(B_y\)) and C (\(C_x\),\(C_y\)) can be written as: area=\(\mod{\frac{A_x(B_yC_y)+B_x(C_yA_y)+C_x(A_yB_y)}{2}}\). Here one of the coordinates is (0,0). Thus the reduced expression in the explanation. Here is great tool to vizualize the same. https://www.mathopenref.com/coordtrianglearea.htmlHi Sandy, It is Question 13 from Quantitative Test 1. I do not think that just graph is the issue. I think either the coordinates or the options also need to change. Even if we are unable to use the formula you or the explanation gave, we should be able to use Area of a parallelogram = bh and both should give the same result. Please explain and correct me if my concept is wrong. Thanks!



GRE Prep Club Legend
Joined: 07 Jun 2014
Posts: 4857
WE: Business Development (Energy and Utilities)
Followers: 111
Kudos [?]:
1854
[0], given: 397

Re: Find the area of a parallelogram [#permalink]
12 Sep 2018, 14:17
Area of a parallelogram = bhDo you mean base \(\times\) height? If so then that is not a a paralleogram but a rectangle.
_________________
Sandy If you found this post useful, please let me know by pressing the Kudos Button
Try our free Online GRE Test



Manager
Joined: 27 Feb 2017
Posts: 189
Followers: 1
Kudos [?]:
53
[0], given: 15

Re: Find the area of a parallelogram [#permalink]
12 Sep 2018, 14:45
sandy wrote: Area of a parallelogram = bh
Do you mean base \(\times\) height? If so then that is not a a paralleogram but a rectangle. Yes Area= base X height. It also says this everywhere. I got it from Barron's book. I also just cross checked using Google. All sources says that Area of a Parallelogram= base X height, where height is at 90 degress with the base.



GRE Prep Club Legend
Joined: 07 Jun 2014
Posts: 4857
WE: Business Development (Energy and Utilities)
Followers: 111
Kudos [?]:
1854
[0], given: 397

Re: Find the area of a parallelogram [#permalink]
13 Sep 2018, 00:09
kruttikaaggarwal wrote: sandy wrote: Area of a parallelogram = bh
Do you mean base \(\times\) height? If so then that is not a a paralleogram but a rectangle. Yes Area= base X height. It also says this everywhere. I got it from Barron's book. I also just cross checked using Google. All sources says that Area of a Parallelogram= base X height, where height is at 90 degress with the base. This question is from coordinate geometry as apposed to regular geometry, so here you cannot use base \(\times\) height. You have to break the paralleogram into two triangle and find the area of each smaller triangle. This is a tough problem by GRE standards but by no means is it beyond GRE level.
_________________
Sandy If you found this post useful, please let me know by pressing the Kudos Button
Try our free Online GRE Test



Manager
Joined: 27 Feb 2017
Posts: 189
Followers: 1
Kudos [?]:
53
[0], given: 15

Re: Find the area of a parallelogram [#permalink]
13 Sep 2018, 06:15
sandy wrote: kruttikaaggarwal wrote: sandy wrote: Area of a parallelogram = bh
Do you mean base \(\times\) height? If so then that is not a a paralleogram but a rectangle. Yes Area= base X height. It also says this everywhere. I got it from Barron's book. I also just cross checked using Google. All sources says that Area of a Parallelogram= base X height, where height is at 90 degress with the base. This question is from coordinate geometry as apposed to regular geometry, so here you cannot use base \(\times\) height. You have to break the paralleogram into two triangle and find the area of each smaller triangle. This is a tough problem by GRE standards but by no means is it beyond GRE level. Oh, alright! Did not know that. Is this applicable only for parallelograms or for other geometric figures as well? Thanks again Sandy!



Director
Joined: 20 Apr 2016
Posts: 864
WE: Engineering (Energy and Utilities)
Followers: 11
Kudos [?]:
645
[0], given: 141

Re: Find the area of a parallelogram [#permalink]
06 Apr 2019, 20:31
kruttikaaggarwal wrote: If the coordinates of point B are (3, 4) and the coordinates of point C are (7, 7), what is the area of the parallelogram? Attachment: The attachment geometry single 002.JPG is no longer available A. 1 B. 2√7 C. 7 D. 8 E. 7√2 . Here, Let join the sides from Point C to point G on Y axis and point F on X axis. The distance from C to G = distance from C to F = 7 The Area of the Square AFCG = \(7^2\) = \(49\) Point D will be the mirror image of point B and co ordinates of Point D = 4,3 Now let consider the \(\triangle FDA\), \(\triangle FDC\), \(\triangle CGB\) and \(\triangle BGA\) Area of \(\triangle FDA\) =\(\frac{1}{2}* 7 * 3 = \frac{21}{2}\) Area of \(\triangle FDC\) = \(\frac{1}{2}* 7 * 3 = \frac{21}{2}\) Area of \(\triangle CGB\) = \(\frac{1}{2} * 7 * 3 = \frac{21}{2}\) Area of \(\triangle BGA\) = \(\frac{1}{2} * 7 * 3 = \frac{21}{2}\) Sum of all the \(\triangle\) = \(\frac{21}{2} * 4 = 42\) Therefore the area of parallelogram = Area of the Square  Area of the sum of All triangles = \(49  42 = 7\)
Attachments
geometry single 002.JPG [ 17.53 KiB  Viewed 178 times ]
geometry single 003.jpg [ 21.04 KiB  Viewed 178 times ]
_________________
If you found this post useful, please let me know by pressing the Kudos Button
Rules for Posting https://greprepclub.com/forum/rulesfor ... 1083.html




Re: Find the area of a parallelogram
[#permalink]
06 Apr 2019, 20:31





