In the rectangular coordinate system Point O has coordinates : GMAT Problem Solving (PS)
Check GMAT Club App Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

It is currently 09 Dec 2016, 11:59
GMAT Club 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.

Close

Request Expert Reply

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

In the rectangular coordinate system Point O has coordinates

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

1 KUDOS received
Senior Manager
Senior Manager
avatar
Joined: 07 Sep 2010
Posts: 336
Followers: 6

Kudos [?]: 638 [1] , given: 136

In the rectangular coordinate system Point O has coordinates [#permalink]

Show Tags

New post 11 Jun 2013, 06:56
1
This post received
KUDOS
7
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

63% (03:11) correct 37% (02:02) wrong based on 232 sessions

HideShow timer Statistics

In the rectangular coordinate system Point O has coordinates (0,0) and Point B has coordinates (4,4) and if point A is equidistant from points O and B and the area of the triangle OAB is 16, which of the following are the possible coordinates of point A.

A. (-2,6)
B. (0,4)
C. (2,-6)
D. (2,6)
E. (4,0)
[Reveal] Spoiler: OA

_________________

+1 Kudos me, Help me unlocking GMAT Club Tests

Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 35932
Followers: 6860

Kudos [?]: 90090 [1] , given: 10413

Re: In the rectangular coordinate system Point O has coordinates [#permalink]

Show Tags

New post 11 Jun 2013, 07:13
1
This post received
KUDOS
Expert's post
2
This post was
BOOKMARKED
imhimanshu wrote:
In the rectangular coordinate system Point O has coordinates (0,0) and Point B has coordinates (4,4) and if point A is equidistant from points O and B and the area of the triangle OAB is 16, which of the following are the possible coordinates of point A.

A. (-2,6)
B. (0,4)
C. (2,-6)
D. (2,6)
E. (4,0)


Look at the diagram below:
Attachment:
Area.png
Area.png [ 11.71 KiB | Viewed 3244 times ]
Since A is equidistant from points O and B, then it must be somewhere on the green line (perpendicular bisector of OB).

(2,-6) and (2,6) are not on that line. If A is at (0,4) or (4,0), then the area is 1/2*4*4=8. Thus A must be at (-2,6).

Answer: A.

Hope it's clear.
_________________

New to the Math Forum?
Please read this: All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Senior Manager
Senior Manager
avatar
Joined: 07 Sep 2010
Posts: 336
Followers: 6

Kudos [?]: 638 [0], given: 136

Re: In the rectangular coordinate system Point O has coordinates [#permalink]

Show Tags

New post 11 Jun 2013, 07:23
Bunuel wrote:
Since A is equidistant from points O and B, then it must be somewhere on the green line (perpendicular bisector of OB).

Thanks Bunuel for the quick response. However, I'm not able to understand the underlying logic in the above statement. I mean, why it is necessary that point A must lie on perpendicular of OB.
Can you please elaborate. I'm pretty weak in coordinate geometry.

Thanks
imhimanshu
_________________

+1 Kudos me, Help me unlocking GMAT Club Tests

Verbal Forum Moderator
Verbal Forum Moderator
User avatar
Joined: 10 Oct 2012
Posts: 631
Followers: 78

Kudos [?]: 1091 [0], given: 136

Premium Member
Re: In the rectangular coordinate system Point O has coordinates [#permalink]

Show Tags

New post 11 Jun 2013, 08:52
1
This post was
BOOKMARKED
imhimanshu wrote:
In the rectangular coordinate system Point O has coordinates (0,0) and Point B has coordinates (4,4) and if point A is equidistant from points O and B and the area of the triangle OAB is 16, which of the following are the possible coordinates of point A.

A. (-2,6)
B. (0,4)
C. (2,-6)
D. (2,6)
E. (4,0)


Assuming the base of the triangle as OB, which is of length \(4\sqrt{2}\), and let the height from A to OB be h-->

\(\frac{1}{2}*4\sqrt{2}*h\) = 16 --> h = \(4\sqrt{2}\). Also, as the point A is equidistant from both O and B, the point A will lie on the perpendicular bisector of the triangle OAB. Thus, h = the distance between the co-ordinates of A and (2,2)[the mid point of the line segment OB]. Only A satisfies for h = \(4\sqrt{2}\)
A.
_________________

All that is equal and not-Deep Dive In-equality

Hit and Trial for Integral Solutions

1 KUDOS received
Manager
Manager
avatar
Status: Training
Joined: 03 Jun 2013
Posts: 90
Location: Canada
GPA: 3.7
Followers: 3

Kudos [?]: 127 [1] , given: 3

GMAT ToolKit User Reviews Badge
Re: In the rectangular coordinate system Point O has coordinates [#permalink]

Show Tags

New post 11 Jun 2013, 15:20
1
This post received
KUDOS
imhimanshu wrote:
why it is necessary that point A must lie on perpendicular of OB


Hey,

Are you familiar with the term 'equidistant', meaning that the distance between OA and AB must be the same?

Imagine that A is some point that lies on the line OB, and A is equidistant from both points. Then A would have to be the midpoint of OB.

Now, extending that idea to find all points that are equidistant from O and B, if you try to plot a few points, you will see that they form a line that intersects the midpoint of OB, and extends to infinite, perpendicular to OB.

Hope that helps a little.
_________________

KUDOS please if my post was useful!

Manager
Manager
avatar
Joined: 16 Oct 2012
Posts: 58
Followers: 0

Kudos [?]: 8 [0], given: 0

Re: In the rectangular coordinate system Point O has coordinates [#permalink]

Show Tags

New post 11 Jun 2013, 15:32
There are three equidistant point:

(0, 4); (4,0); (-2;6)

Only the last one fulfills the area requirement!
1 KUDOS received
Manager
Manager
avatar
Joined: 13 Aug 2012
Posts: 118
Followers: 0

Kudos [?]: 55 [1] , given: 118

Re: In the rectangular coordinate system Point O has coordinates [#permalink]

Show Tags

New post 02 Aug 2013, 09:18
1
This post received
KUDOS
another way the question can be solved is by using the distance forumula
Since, \(AO=AB\), their distance will be the same, therefore by using the formula we get \(x^2+y^2=(x-4)^2+(y-4)^2\)
Solving the above equation, we get \(x+y=4\). Now the only option that satisfies this equation is A.

Hope this helps
Manager
Manager
avatar
Joined: 13 Aug 2012
Posts: 118
Followers: 0

Kudos [?]: 55 [0], given: 118

Re: In the rectangular coordinate system Point O has coordinates [#permalink]

Show Tags

New post 02 Aug 2013, 09:24
Bunuel wrote:
imhimanshu wrote:
In the rectangular coordinate system Point O has coordinates (0,0) and Point B has coordinates (4,4) and if point A is equidistant from points O and B and the area of the triangle OAB is 16, which of the following are the possible coordinates of point A.

A. (-2,6)
B. (0,4)
C. (2,-6)
D. (2,6)
E. (4,0)


Look at the diagram below:
Attachment:
Area.png
Since A is equidistant from points O and B, then it must be somewhere on the green line (perpendicular bisector of OB).

(2,-6) and (2,6) are not on that line. If A is at (0,4) or (4,0), then the area is 1/2*4*4=8. Thus A must be at (-2,6).

Answer: A.

Hope it's clear.


I was wondering, since we wouldn't be provided with a graph paper and can only draw a rough figure, how would one exactly come to know the middle point of the line OB?
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 12904
Followers: 562

Kudos [?]: 158 [0], given: 0

Premium Member
Re: In the rectangular coordinate system Point O has coordinates [#permalink]

Show Tags

New post 20 Sep 2014, 03:58
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 12904
Followers: 562

Kudos [?]: 158 [0], given: 0

Premium Member
Re: In the rectangular coordinate system Point O has coordinates [#permalink]

Show Tags

New post 01 Aug 2016, 03:26
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Manager
Manager
avatar
Joined: 22 Feb 2016
Posts: 83
Location: India
Concentration: Economics, Healthcare
GMAT 1: 690 Q42 V47
GMAT 2: 710 Q47 V39
GPA: 3.57
Followers: 1

Kudos [?]: 5 [0], given: 185

Re: In the rectangular coordinate system Point O has coordinates [#permalink]

Show Tags

New post 15 Oct 2016, 20:16
Another way of solving this.

When we draw the given senerio we realise for A to be equidistant to both o and B it needs to be on the 2nd or 4th quadrant. only option in the second quadrant is A

hence A
Expert Post
VP
VP
User avatar
Joined: 08 Jul 2010
Posts: 1432
Location: India
GMAT: INSIGHT
WE: Education (Education)
Followers: 65

Kudos [?]: 1343 [0], given: 42

Re: In the rectangular coordinate system Point O has coordinates [#permalink]

Show Tags

New post 15 Oct 2016, 21:09
AmritaSarkar89 wrote:
Another way of solving this.

When we draw the given senerio we realise for A to be equidistant to both o and B it needs to be on the 2nd or 4th quadrant. only option in the second quadrant is A

hence A



There is an option which shows a point in 4th Quadrant (which one should notice even if one goes by quick observation like you have shown) however that is much closer to O than point B so that can't be the correct option.

Your approach is really good. exactly like one needed in any aptitude test. Overlooking option would be too bad for anyone taking GMAT
_________________

Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com
Call us : +91-9999687183 / 9891333772
http://www.GMATinsight.com/testimonials.html



Feel free to give a Kudos if it is a useful post .

Re: In the rectangular coordinate system Point O has coordinates   [#permalink] 15 Oct 2016, 21:09
    Similar topics Author Replies Last post
Similar
Topics:
4 Experts publish their posts in the topic In the rectangular coordinate system shown above, points O, P, and Q r AbdurRakib 3 23 Jun 2016, 11:15
6 In a rectangular coordinate system, if a line passes through the point vatsavayi 4 23 Oct 2014, 00:17
6 Experts publish their posts in the topic In the rectangular coordinate system above, if point R (not Walkabout 4 27 Dec 2012, 05:18
43 Experts publish their posts in the topic In a rectangular coordinate system, point A has coordinates Financier 19 20 Aug 2010, 13:30
44 Experts publish their posts in the topic In the rectangular coordinate system, points (4, 0) and Bunuel 22 11 Nov 2009, 12:13
Display posts from previous: Sort by

In the rectangular coordinate system Point O has coordinates

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.