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.
Join timely conversations and get much-needed information about your educational future in our free event series. The sessions will focus on a variety of topics, from going to college in a pandemic to racial inequality in education.
Parallelogram OPQR lies in the xy-plane [#permalink]
27 Dec 2015, 19:42
2
This post received KUDOS
Expert's post
00:00
Question Stats:
86% (03:42) correct
13% (01:59) wrong based on 134 sessions
Attachment:
#GREpracticequestion Parallelogram OPQR lies in the xy-plane.jpg [ 15.64 KiB | Viewed 6168 times ]
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
Re: Parallelogram OPQR lies in the xy-plane [#permalink]
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)
Re: Parallelogram OPQR lies in the xy-plane [#permalink]
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.
Re: Parallelogram OPQR lies in the xy-plane [#permalink]
20 Mar 2018, 13:27
6
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 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
From here, it we can determine the coordinates of point R
Answer: E
RELATED VIDEO FROM MY COURSE
_________________
Brent Hanneson – Creator of greenlighttestprep.com If you enjoy my solutions, you'll like my GRE prep course. Sign up for GRE Question of the Dayemails
Re: Parallelogram OPQR lies in the xy-plane [#permalink]
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).
close
86% (03:42) correct
