GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 15 Dec 2018, 21:54

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

Confirm Cancel
Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
  • $450 Tuition Credit & Official CAT Packs FREE

     December 15, 2018

     December 15, 2018

     10:00 PM PST

     11:00 PM PST

    Get the complete Official GMAT Exam Pack collection worth $100 with the 3 Month Pack ($299)
  • FREE Quant Workshop by e-GMAT!

     December 16, 2018

     December 16, 2018

     07:00 AM PST

     09:00 AM PST

    Get personalized insights on how to achieve your Target Quant Score.

What is the equation that represents the locus of points equidistant

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

Hide Tags

VP
VP
User avatar
Joined: 18 May 2008
Posts: 1109
What is the equation that represents the locus of points equidistant  [#permalink]

Show Tags

New post 24 Jun 2008, 02:20
6
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

57% (02:12) correct 43% (02:10) wrong based on 91 sessions

HideShow timer Statistics

What is the equation that represents the locus of points equidistant from the points A (-2, 1) and B (6, 3)?

(A) 4x+y=20
(B) y+4x=10
(C) 4y+x=10
(D) y+2x=20
(E) x+4y=40
Current Student
User avatar
Joined: 12 Jun 2008
Posts: 286
Schools: INSEAD Class of July '10
Re: What is the equation that represents the locus of points equidistant  [#permalink]

Show Tags

New post 24 Jun 2008, 02:35
Answer is (B)

The locus of points equidistant from 2 points is the perpendicular bisector of the segment between these 2 points.

Vector AB is (8,2) and we want a vector (x,y) which is normal to that one (it will give the direction of the perpendicular bisector).

Their dot product has to be null, so we get 8x+2y=0, which is equal to 4x+y=0

Therefore any line with equation 4x+y=K is perpendicular to the line that goes through A and B.

Answer is then either (A) or (B).

If the line we are looking for is the locus of points equidistant from A and B, it contains the middle point between A and B, which is M(2,2).

This point verifies 4x+y=10: (B) is the answer.
Director
Director
avatar
Joined: 14 Aug 2007
Posts: 676
Re: What is the equation that represents the locus of points equidistant  [#permalink]

Show Tags

New post 24 Jun 2008, 04:39
ritula wrote:
What is the equation that represents the locus of points equidistant from the points A (-2, 1) and B (6, 3)?
(A) 4x+y=20
(B) y+4x=10
(C) 4y+x=10
(D) y+2x=20
(E) x+4y=40
I know that its pretty simple question, but sumhow im not getting the right answer. pls help!


B

[x-(-2)]^2 + [y -1]^2 = [x-6]^2 + [y-3]^2

the squared terms on both sides get cancelled leaving us with B
SVP
SVP
User avatar
Joined: 30 Apr 2008
Posts: 1826
Location: Oklahoma City
Schools: Hard Knocks
Re: What is the equation that represents the locus of points equidistant  [#permalink]

Show Tags

New post 24 Jun 2008, 04:56
1
Maybe I just like to work harder than everyone else. Here is how I arrived at B.

Locus = perpendicular bisector.

Find the mid point between A & B. 6 - -2 = 8 and 3 - 1 = 2, so go right 8 and up 2, so midpoint is half that. Go right 4, and up 1. Brings us to {2, 2}. Slope of AB is 1/4 because rise over run 2 up 8 right = \(\frac{2}{8}\) or \(\frac{1}{4}\).

The prependicular line to this will be inverted and the sign flipped. Inverse of 1/4 is 4/1 and negative is -4. To find the x-intercept you have to move left from 2,2 so go up 4, but left, or negative 1. (If you have 4/1, if you move in a positive direction for one of the numbers 4 or 1, the other must move in a negative direction). Up 4 and left 1 brings you to point 1, 6, that's not the x yet, so up 4 and left 1 again brings us to 0 ,10. x-intercept of +10.

Now this perpendicular line is represented by the equation y = -4x + 10. Find the answer that will give you that when solved for y. This is B

y + 4x = 10
y = 10 - 4x or
y = -4x +10

ritula wrote:
What is the equation that represents the locus of points equidistant from the points A (-2, 1) and B (6, 3)?
(A) 4x+y=20
(B) y+4x=10
(C) 4y+x=10
(D) y+2x=20
(E) x+4y=40
I know that its pretty simple question, but sumhow im not getting the right answer. pls help!

_________________

------------------------------------
J Allen Morris
**I'm pretty sure I'm right, but then again, I'm just a guy with his head up his a$$.

GMAT Club Premium Membership - big benefits and savings

VP
VP
User avatar
Joined: 18 May 2008
Posts: 1109
Re: What is the equation that represents the locus of points equidistant  [#permalink]

Show Tags

New post 24 Jun 2008, 22:00
OA is B indeed. i was doing the big mistake of keeping its slope the same as the given line while actually it is a perpendicular line. Thanks to all!
Manager
Manager
avatar
B
Joined: 22 Nov 2014
Posts: 60
What is the equation that represents the locus of points equidistant f  [#permalink]

Show Tags

New post 12 May 2016, 17:49
What is the equation that represents the locus of points equidistant from the points A (-2,1) and B (6,3)

A) 4x+y = 20
B) y+4x = 10
C) 4y+x = 10
D) y+2x = 20
E) x+4y = 20

My Solution is to find the slope of line AB, which is equal to 1/4. The equation of locus of points asked thus will have a slope of -4.

That itself allows me to reject C,D and E
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 7108
Re: What is the equation that represents the locus of points equidistant f  [#permalink]

Show Tags

New post 12 May 2016, 19:40
2
2
ruchi857 wrote:
What is the equation that represents the locus of points equidistant from the points A (-2,1) and B (6,3)

A) 4x+y = 20
B) y+4x = 10
C) 4y+x = 10
D) y+2x = 20
E) x+4y = 20

My Solution is to find the slope of line AB, which is equal to 1/4. The equation of locus of points asked thus will have a slope of -4.

That itself allows me to reject C,D and E


hi,

you can work on two issues and get your answer..



1) A (-2,1) and B (6,3)..
therefore a point equidistant from BOTH will be there average..
so\(x = \frac{-2+6}{2}= 2\) and \(y =\frac{1+3}{2} = 2\)..
substitute x as 2 and y as 2 and see which equation satisfies the values...
ONLY B and C are left..

2) As shown by you, work on slope..
slope of line AB =\(\frac{3-1}{6-(-2)} = \frac{2}{8} = \frac{1}{4}\)..
so slope of line joining all points = -4, as this line will be perpendicular to AB...
ONLY A and B satisfy the condition

ONLY B satisfies both points..
ans B
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


GMAT online Tutor

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 51218
Re: What is the equation that represents the locus of points equidistant  [#permalink]

Show Tags

New post 12 May 2016, 23:17
ruchi857 wrote:
What is the equation that represents the locus of points equidistant from the points A (-2,1) and B (6,3)

A) 4x+y = 20
B) y+4x = 10
C) 4y+x = 10
D) y+2x = 20
E) x+4y = 20

My Solution is to find the slope of line AB, which is equal to 1/4. The equation of locus of points asked thus will have a slope of -4.

That itself allows me to reject C,D and E

____________________
Merging topics.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | 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

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 9179
Premium Member
Re: What is the equation that represents the locus of points equidistant  [#permalink]

Show Tags

New post 24 Sep 2018, 06:44
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 Bot
Re: What is the equation that represents the locus of points equidistant &nbs [#permalink] 24 Sep 2018, 06:44
Display posts from previous: Sort by

What is the equation that represents the locus of points equidistant

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


Copyright

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

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

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®.