Last visit was: 30 Apr 2026, 12:42 It is currently 30 Apr 2026, 12:42
Home
Messages
Tests
Schools
Events
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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
User avatar
mikemcgarry
User avatar
Magoosh GMAT Instructor
Joined: 28 Dec 2011
Last visit: 06 Aug 2018
Posts: 4,474
Own Kudos:
30,895
 [36]
Given Kudos: 130
Expert
Expert reply
Posts: 4,474
Kudos: 30,895
 [36]
In a coordinate system, P = (2, 7) and Q = (2, 3). Which c 01 Aug 2014, 13:25
4
Kudos
Add Kudos
32
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

95% (hard)

Question Stats:

41% (02:45) correct 59% (02:39) wrong based on 329 sessions

History

Date
Time
Result
Not Attempted Yet
In a coordinate system, P = (2, 7) and Q = (2, –3). Which could be the coordinates of R if PQR is an isosceles triangle?

I. (12, –3)
II. (–6, –9)
III. (–117, 2)

(A) I only
(B) I and II only
(C) I and III only
(D) II and III only
(E) I, II, and III

Show Spoiler
For a set of seven other challenging Coordinate Geometry problems, as well as the OE with diagrams for this question, see:
https://magoosh.com/gmat/2014/challengi ... questions/

Mike ­
ShowHide Answer
Official Answer
E
Most Helpful Reply
avatar
stoneshwar
avatar
Joined: 03 Jul 2014
Last visit: 28 Oct 2014
Posts: 9
Own Kudos:
15
 [5]
Schools: Sloan '17 (S) Stanford '17 (S)
GMAT 1: 760 Q49 V42
Schools: Sloan '17 (S) Stanford '17 (S)
GMAT 1: 760 Q49 V42
Posts: 9
Kudos: 15
 [5]
In a coordinate system, P = (2, 7) and Q = (2, 3). Which c 01 Aug 2014, 22:57
4
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
PQ's length is 10.

1. QR is also 10.
2. Pythagorean triplet, again QR is 10.
3. y=2 is a bisector of QR so anything on this line will create an isosceles triangle.

So E I, II and III
General Discussion
User avatar
fskilnik
User avatar
Joined: 12 Oct 2010
Last visit: 03 Jan 2025
Posts: 883
Own Kudos:
1,890
 [4]
Given Kudos: 57
Status:GMATH founder
Expert
Expert reply
Posts: 883
Kudos: 1,890
 [4]
In a coordinate system, P = (2, 7) and Q = (2, 3). Which c 25 Sep 2018, 12:39
3
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
stoneshwar
PQ's length is 10.

1. QR is also 10.
2. Pythagorean triplet, again QR is 10.
3. y=2 is a bisector of QR so anything on this line will create an isosceles triangle.

So E I, II and III
Show more
Perfect! Those arguments deserve the corresponding image (attached).

Regards,
Fabio.
Attachments

25Set18_4w.gif
25Set18_4w.gif [ 11.79 KiB | Viewed 10207 times ]

User avatar
PinakiRDas
User avatar
Joined: 07 Jan 2012
Last visit: 22 Jan 2020
Posts: 45
Own Kudos:
18
Given Kudos: 72
Location: Canada
Concentration: International Business, Entrepreneurship
GMAT Date: 04-30-2012
WE:Information Technology (Computer Software)
Posts: 45
Kudos: 18
In a coordinate system, P = (2, 7) and Q = (2, 3). Which c 26 Sep 2018, 18:37
Kudos
Add Kudos
Bookmarks
Bookmark this Post
fskilnik
stoneshwar
PQ's length is 10.

1. QR is also 10.
2. Pythagorean triplet, again QR is 10.
3. y=2 is a bisector of QR so anything on this line will create an isosceles triangle.

So E I, II and III
Perfect! Those arguments deserve the corresponding image (attached).

Regards,
Fabio.
Show more
2 Questions here:
1. Can we apply the triplet rule without knowing for sure if 1 angle in 90? Or other way round can this triplet be applied on any triangle?
2. How can we rule out the possibility that PR = QR?

TIA
User avatar
fskilnik
User avatar
Joined: 12 Oct 2010
Last visit: 03 Jan 2025
Posts: 883
Own Kudos:
1,890
Given Kudos: 57
Status:GMATH founder
Expert
Expert reply
Posts: 883
Kudos: 1,890
In a coordinate system, P = (2, 7) and Q = (2, 3). Which c 26 Sep 2018, 19:51
Kudos
Add Kudos
Bookmarks
Bookmark this Post
PinakiRDas

2 Questions here:
1. Can we apply the triplet rule without knowing for sure if 1 angle in 90? Or other way round can this triplet be applied on any triangle?
2. How can we rule out the possibility that PR = QR?
Show more
Hi, PinakiRDas.

1. No! In the figure in the middle, the fact that there is a 90-degrees angle "formed" by the sides with lengths 6 and 8 is necessary to be able to conclude that the other side (the hypotenuse) is 10 units of length. More explicitly: you have a (non-right) triangle with sides 6,8 and 10.1, for instance.
2. Any equilateral triangle is also an isosceles triangle. An isosceles triangle, by definition, has (at least) two sides with same lengths.

Regards,
Fabio.
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 39,011
Own Kudos:
1,122
Posts: 39,011
Kudos: 1,122
In a coordinate system, P = (2, 7) and Q = (2, 3). Which c 02 Jul 2024, 08:23
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.
Moderators:
Bunuel
Math Expert
110017 posts
Krunaal
Tuck School Moderator
852 posts