Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

It is currently 19 Jul 2019, 16:03

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

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

Find Similar Topics 
VP
VP
User avatar
Joined: 18 May 2008
Posts: 1043
What is the equation that represents the locus of points equidistant  [#permalink]

Show Tags

New post 24 Jun 2008, 03:20
1
9
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

62% (02:12) correct 38% (02:08) wrong based on 85 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
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 7764
Re: What is the equation that represents the locus of points equidistant f  [#permalink]

Show Tags

New post 12 May 2016, 20:40
2
3
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
_________________
General Discussion
Current Student
User avatar
Joined: 12 Jun 2008
Posts: 278
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, 03:35
1
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: 635
Re: What is the equation that represents the locus of points equidistant  [#permalink]

Show Tags

New post 24 Jun 2008, 05:39
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
B
Joined: 30 Apr 2008
Posts: 1782
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, 05:56
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: 1043
Re: What is the equation that represents the locus of points equidistant  [#permalink]

Show Tags

New post 24 Jun 2008, 23:00
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: 23 Nov 2014
Posts: 60
What is the equation that represents the locus of points equidistant f  [#permalink]

Show Tags

New post 12 May 2016, 18:49
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 Sep 2009
Posts: 56300
Re: What is the equation that represents the locus of points equidistant  [#permalink]

Show Tags

New post 13 May 2016, 00:17
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.
_________________
Manager
Manager
User avatar
S
Joined: 30 May 2018
Posts: 82
GMAT 1: 620 Q42 V34
WE: Corporate Finance (Commercial Banking)
Re: What is the equation that represents the locus of points equidistant  [#permalink]

Show Tags

New post 28 Apr 2019, 11:20
chetan2u wrote:
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



chetan2u Could you please explain the red part.
GMAT Club Bot
Re: What is the equation that represents the locus of points equidistant   [#permalink] 28 Apr 2019, 11:20
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  





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