Jul 19 08:00 AM PDT  09:00 AM PDT The Competition Continues  Game of Timers is a teambased competition based on solving GMAT questions to win epic prizes! Starting July 1st, compete to win prep materials while studying for GMAT! Registration is Open! Ends July 26th Jul 20 07:00 AM PDT  09:00 AM PDT Attend this webinar and master GMAT SC in 10 days by learning how meaning and logic can help you tackle 700+ level SC questions with ease. Jul 21 07:00 AM PDT  09:00 AM PDT Attend this webinar to learn a structured approach to solve 700+ Number Properties question in less than 2 minutes
Author 
Message 
TAGS:

Hide Tags

Director
Status: I don't stop when I'm Tired,I stop when I'm done
Joined: 11 May 2014
Posts: 530
Location: Bangladesh
Concentration: Finance, Leadership
GPA: 2.81
WE: Business Development (Real Estate)

In the rectangular coordinate system shown above, points O, P, and Q r
[#permalink]
Show Tags
23 Jun 2016, 12:15
Question Stats:
78% (01:38) correct 22% (01:58) wrong based on 618 sessions
HideShow timer Statistics
In the rectangular coordinate system shown above, points O, P, and Q represent the sites of three proposed housing developments. If a fire station can be built at any point in the coordinate system, at which point would it be equidistant from all three developments? A. (3,1) B. (1,3) C. (3,2) D. (2,2) E. (2,3) OG Q 2017(Book Question: 24) Attachment:
24xj68n.jpg [ 11.54 KiB  Viewed 1457 times ]
Official Answer and Stats are available only to registered users. Register/ Login.
_________________




Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9442
Location: Pune, India

Re: In the rectangular coordinate system shown above, points O, P, and Q r
[#permalink]
Show Tags
24 Jun 2016, 01:16
AbdurRakib wrote: In the rectangular coordinate system shown above, points O, P, and Q represent the sites of three proposed housing developments. If a fire station can be built at any point in the coordinate system, at which point would it be equidistant from all three developments? A. (3,1) B. (1,3) C. (3,2) D. (2,2) E. (2,3) OG Q 2017(Book Question: 24) All points equidistant from O and Q lie on the line x = 2 so the fire station should lie on this line. All points equidistant from O and P lie on the line y = 3 so the fire station should lie on this line too. These two intersect at (2, 3) and that will be the point equidistant from all 3 points. Answer (E) Or You can think of the question in terms of the perpendicular bisectors of triangle OPQ. Their point of intersection will be equidistant from all three vertices. Again the perpendicular bisector of OQ will be x = 2 and of OP will be y = 3. They will intersect at (2, 3). Answer (E)
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >




Senior Manager
Joined: 23 Apr 2015
Posts: 295
Location: United States
Concentration: General Management, International Business
WE: Engineering (Consulting)

Re: In the rectangular coordinate system shown above, points O, P, and Q r
[#permalink]
Show Tags
23 Jun 2016, 15:05
Answer is E : (2,3)
the point we're asked is the Centroid of the triangle (scalene). Let it be (x,y). Then it should have same distance from all three points.So using the Pythagoras theorem of distance between 2 points: distance from origin = distance from (4,0) \(\sqrt{(x^2 + y^2)} = \sqrt{((4x)^2 + y^2)}\)
distance from origin = distance from (0,6) \(\sqrt{(x^2 + y^2)} = \sqrt{(x^2 + (6y)^2)}\)
Solve these 2 for x and y and it will give (2,3)
(Share a kudo's , if you like the explanation)



Intern
Joined: 03 Jun 2016
Posts: 10

Re: In the rectangular coordinate system shown above, points O, P, and Q r
[#permalink]
Show Tags
24 Jun 2016, 02:20
The point should be the circumcentre of the triangle and in right angled triangle circumcentre lies on hypotenuse and is midpoint of it . Therefore it can be directly seen that mid point of the hypotenuse will be E.(2,3).



Intern
Joined: 01 Mar 2017
Posts: 12

Re: In the rectangular coordinate system shown above, points O, P, and Q r
[#permalink]
Show Tags
07 Apr 2017, 10:33
VeritasPrepKarishma wrote: AbdurRakib wrote: In the rectangular coordinate system shown above, points O, P, and Q represent the sites of three proposed housing developments. If a fire station can be built at any point in the coordinate system, at which point would it be equidistant from all three developments? A. (3,1) B. (1,3) C. (3,2) D. (2,2) E. (2,3) OG Q 2017(Book Question: 24) All points equidistant from O and Q lie on the line x = 2 so the fire station should lie on this line. All points equidistant from O and P lie on the line y = 3 so the fire station should lie on this line too. These two intersect at (2, 3) and that will be the point equidistant from all 3 points. Answer (E) Or You can think of the question in terms of the perpendicular bisectors of triangle OPQ. Their point of intersection will be equidistant from all three vertices. Again the perpendicular bisector of OQ will be x = 2 and of OP will be y = 3. They will intersect at (2, 3). Answer (E) Is it a general fact, that bisectors of the two legs of a right triangle will cut the hypotenuse exactly in half, in other words, intersect the hypotenuse at its midpoint?



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9442
Location: Pune, India

Re: In the rectangular coordinate system shown above, points O, P, and Q r
[#permalink]
Show Tags
09 Apr 2017, 22:42
melin94 wrote: VeritasPrepKarishma wrote: AbdurRakib wrote: In the rectangular coordinate system shown above, points O, P, and Q represent the sites of three proposed housing developments. If a fire station can be built at any point in the coordinate system, at which point would it be equidistant from all three developments? A. (3,1) B. (1,3) C. (3,2) D. (2,2) E. (2,3) OG Q 2017(Book Question: 24) All points equidistant from O and Q lie on the line x = 2 so the fire station should lie on this line. All points equidistant from O and P lie on the line y = 3 so the fire station should lie on this line too. These two intersect at (2, 3) and that will be the point equidistant from all 3 points. Answer (E) Or You can think of the question in terms of the perpendicular bisectors of triangle OPQ. Their point of intersection will be equidistant from all three vertices. Again the perpendicular bisector of OQ will be x = 2 and of OP will be y = 3. They will intersect at (2, 3). Answer (E) Is it a general fact, that bisectors of the two legs of a right triangle will cut the hypotenuse exactly in half, in other words, intersect the hypotenuse at its midpoint? Yes, that is correct. The circumcenter of a right triangle (the point of intersection of perpendicular bisectors) will bisect the hypotenuse.
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



Math Expert
Joined: 02 Sep 2009
Posts: 56272

Re: In the rectangular coordinate system shown above, points O, P, and Q r
[#permalink]
Show Tags
09 Apr 2017, 23:48
VeritasPrepKarishma wrote: melin94 wrote: VeritasPrepKarishma wrote: All points equidistant from O and Q lie on the line x = 2 so the fire station should lie on this line. All points equidistant from O and P lie on the line y = 3 so the fire station should lie on this line too. These two intersect at (2, 3) and that will be the point equidistant from all 3 points.
Answer (E)
Or You can think of the question in terms of the perpendicular bisectors of triangle OPQ. Their point of intersection will be equidistant from all three vertices. Again the perpendicular bisector of OQ will be x = 2 and of OP will be y = 3. They will intersect at (2, 3). Answer (E)
Is it a general fact, that bisectors of the two legs of a right triangle will cut the hypotenuse exactly in half, in other words, intersect the hypotenuse at its midpoint? Yes, that is correct. The circumcenter of a right triangle (the point of intersection of perpendicular bisectors) will bisect the hypotenuse. Another way to phrase this property is: in a right triangle, the median drawn to the hypotenuse has the measure half the hypotenuse.
_________________



Manager
Joined: 10 Sep 2014
Posts: 78
Location: Bangladesh
GPA: 3.5
WE: Project Management (Manufacturing)

Re: In the rectangular coordinate system shown above, points O, P, and Q r
[#permalink]
Show Tags
23 Mar 2018, 04:44
I followed the midpoint property of coordinate geometry and got the same result. Is there any problem ? Bunuel, VeritasPrepKarishma, chetan2u, JeffTargetTestPrep, GMATPrepNow.



Current Student
Joined: 28 Oct 2017
Posts: 32
Location: India
GMAT 1: 640 Q47 V32 GMAT 2: 710 Q49 V38

Re: In the rectangular coordinate system shown above, points O, P, and Q r
[#permalink]
Show Tags
22 Jul 2018, 21:32
All three points would be on the periphery of a circle while the fire station would be at the center. So, (Xa)^2+(Yb)^2=C^2, where (a,b) are the three points. Solving three equations we get (X,Y) as (2,3).



Intern
Joined: 01 May 2017
Posts: 36

Re: In the rectangular coordinate system shown above, points O, P, and Q r
[#permalink]
Show Tags
05 Jan 2019, 02:39
Use Centroid of Triangle formula.
Centroid of Triangle is (x1+x2+x3)/3, (y1+y2+y3)/3
here, X and Y are points of triangle.



Senior Manager
Joined: 10 Apr 2018
Posts: 270
Location: United States (NC)

Re: In the rectangular coordinate system shown above, points O, P, and Q r
[#permalink]
Show Tags
10 Jan 2019, 12:44
sunngupt11 wrote: Use Centroid of Triangle formula.
Centroid of Triangle is (x1+x2+x3)/3, (y1+y2+y3)/3
here, X and Y are points of triangle. Well sunngupt11, If you use centroid formula you get\(\frac {4}{3}\), \(\frac {6}{3}\) Also centroid of triangle lies inside the triangle. If you look at the responses above many have solved this using circumradius or perpendicular bisectors of triangle. Now the three perpendicular bisectors of triangle can meet inside the triangle or outside the triangle . I guess what must have confused you is that centroid divides the media in a ratio of 2:1. but that dosen't mean all the medians of a triangle will be of equal length.
_________________
Probus
~You Just Can't beat the person who never gives up~ Babe Ruth



Manager
Joined: 12 Apr 2017
Posts: 116
Location: United States
Concentration: Finance, Operations
GPA: 3.1

In the rectangular coordinate system shown above, points O, P, and Q r
[#permalink]
Show Tags
10 Jul 2019, 13:46
knowing that it is a right triangle, is using the midpoint formula suitable?
(X1 + x2)/ 2, (y1+y2)/2
(0 + 4) / 2 , (0 + 6) / 2
2,3




In the rectangular coordinate system shown above, points O, P, and Q r
[#permalink]
10 Jul 2019, 13:46






