It is currently 18 Nov 2018, 23:43
My Tests

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Parallelogram OPQR lies in the xy-plane

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
1 KUDOS received
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 07 Jun 2014
Posts: 4711
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 91

Kudos [?]: 1615 [1] , given: 376

CAT Tests
Parallelogram OPQR lies in the xy-plane [#permalink] New post 27 Dec 2015, 19:42
1
This post received
KUDOS
Expert's post
00:00

Question Stats:

78% (01:48) correct 21% (01:54) wrong based on 23 sessions
Image

Parallelogram OPQR lies in the xy-plane, as shown in the figure above. The coordinates of point P are (2, 4) and the coordinates of point Q are (8, 6). What are the coordinates of point R ?

A. (3, 2)
B. (3, 3)
C. (4, 4)
D. (5, 2)
E. (6, 2)

Practice Questions
Question: 10
Page: 158
Difficulty: hard


[Reveal] Spoiler: image
Attachment:
Quant.jpg
Quant.jpg [ 15.64 KiB | Viewed 5881 times ]
[Reveal] Spoiler: OA

_________________

Sandy
If you found this post useful, please let me know by pressing the Kudos Button

Try our free Online GRE Test

1 KUDOS received
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 07 Jun 2014
Posts: 4711
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 91

Kudos [?]: 1615 [1] , given: 376

CAT Tests
Re: Parallelogram OPQR lies in the xy-plane [#permalink] New post 27 Dec 2015, 20:00
1
This post received
KUDOS
Expert's post
Here we have a parallelogram OPQR. So PQ has the same length as OR. PQ is (2,4) and (8,6).
Length of PQ = \(\sqrt{(8-2)^2 + (6 -4)^2}\) .

PQ =\(\sqrt{(6)^2 + (2)^2}\)=\(\sqrt{40}\).

Only option E (6,2) holds correct.
_________________

Sandy
If you found this post useful, please let me know by pressing the Kudos Button

Try our free Online GRE Test

Intern
Intern
Joined: 28 Mar 2016
Posts: 11
Followers: 0

Kudos [?]: 0 [0], given: 0

Re: Parallelogram OPQR lies in the xy-plane [#permalink] New post 29 Mar 2016, 09:26
is (6,2) the square root of 40 simplified?
1 KUDOS received
Intern
Intern
Joined: 22 Mar 2016
Posts: 12
Followers: 0

Kudos [?]: 9 [1] , given: 1

Re: Parallelogram OPQR lies in the xy-plane [#permalink] New post 27 Apr 2016, 08:27
1
This post received
KUDOS
It is a parallelogram. If the distance between O to P in “X”axis is 2, the distance between R to Q in “X” axis must be 2. So, Distance between O to R in “X” axis will be 8-2= 6. Similarly, If the distance between O to P in “Y”axis is 4, the distance between Q to R in “Y” axis must be 4. So, Distance between O to R in “Y” axis will be 6-4= 2. The point at R= (6,2)
1 KUDOS received
Manager
Manager
Joined: 23 Jan 2016
Posts: 137
Followers: 3

Kudos [?]: 108 [1] , given: 15

Re: Parallelogram OPQR lies in the xy-plane [#permalink] New post 29 May 2016, 23:18
1
This post received
KUDOS
As OPQR is a parallelogram, OQ and PR bisects each other. The mid point of OQ is (4,3). Now the slope of PR is -1/2. So the coordinate of R is (6,2)
1 KUDOS received
Director
Director
Joined: 03 Sep 2017
Posts: 521
Followers: 1

Kudos [?]: 327 [1] , given: 66

Re: Parallelogram OPQR lies in the xy-plane [#permalink] New post 15 Sep 2017, 00:14
1
This post received
KUDOS
I have used the fact that PQ and OR must be parallel since the figure is a parallelogram, then the slope of PQ must be the same as OR. The slope of PQ is equal to 1/3, thus, given that O=(0,0), R must be equal to (6,2) in order to have a slope of 1/3, i.e. (2-0)/(6-0) = 1/3.
2 KUDOS received
GRE Instructor
User avatar
Joined: 10 Apr 2015
Posts: 1177
Followers: 44

Kudos [?]: 1054 [2] , given: 6

CAT Tests
Re: Parallelogram OPQR lies in the xy-plane [#permalink] New post 20 Mar 2018, 13:27
2
This post received
KUDOS
Expert's post
sandy wrote:

Parallelogram OPQR lies in the xy-plane, as shown in the figure above. The coordinates of point P are (2, 4) and the coordinates of point Q are (8, 6). What are the coordinates of point R ?

A. (3, 2)
B. (3, 3)
C. (4, 4)
D. (5, 2)
E. (6, 2)



KEY CONCEPT: Since OPQR is a parallelogram, we know that sides PQ and OR are parallel AND the same length

Let's take a closer look at side PQ
Image
Notice that, to get from point P to point Q we must move 2 units UP and move 6 units RIGHT.

Since sides PQ and OR are parallel AND the same length, the same must apply to points O and R
So, if we start from point O (at 0,0) and move 2 units UP and move 6 units RIGHT, we must get to point R
Image

From here, it we can determine the coordinates of point R
Image

Answer: E



RELATED VIDEO FROM OUR COURSE

_________________

Brent Hanneson – Creator of greenlighttestprep.com
Image
Sign up for our free GRE Question of the Day emails

Intern
Intern
Joined: 27 Jun 2018
Posts: 2
Followers: 0

Kudos [?]: 1 [0], given: 0

Re: Parallelogram OPQR lies in the xy-plane [#permalink] New post 27 Jun 2018, 20:47
The slope of the line from the origin to point P is the same as the slope of the line from point Q to R because we have a parallelgram. The same is true for the lines between points P and Q and the origin and point R. The slope of the line from the origin to P is 2, so it follows that the slope of the line between between Q and R is also 2. Now we can determine the equations of the lines between the origin and R and also between Q and R. Given points P and Q, it is easy to see that the slope line between these points is 1/3. It follows that the slope of the line between the origin and R is also 1/3. Hence, the equation of the line from the origin to R is y=1/3X. Using the fact that the slope of the line between Q and R is 2 and we are given that the coordinates of Q are (8,6), we can determine the equation of the line between Q and R to be Y=2X-10 using the point-slope method. We can determine the coordinates of R by setting the equations of the lines Y=1/3X and Y=2X-10 together. Solve for X: 1/3X=2X-10, So X is 6. Plug 6 into Y=1/3X or Y=2X-10 to get Y=2. Answer: (6,2).
Re: Parallelogram OPQR lies in the xy-plane   [#permalink] 27 Jun 2018, 20:47
Display posts from previous: Sort by

Parallelogram OPQR lies in the xy-plane

  Question banks Downloads My Bookmarks Reviews Important topics  


GRE Prep Club Forum Home| About| Terms and Conditions and Privacy Policy| GRE Prep Club Rules| Contact

Powered by phpBB © phpBB Group

Kindly note that the GRE® test is a registered trademark of the Educational Testing Service®, and this site has neither been reviewed nor endorsed by ETS®.