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• ### $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 Joined: 18 May 2008 Posts: 1109 What is the equation that represents the locus of points equidistant [#permalink] ### Show Tags 24 Jun 2008, 02:20 6 00:00 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 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 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 Joined: 14 Aug 2007 Posts: 676 Re: What is the equation that represents the locus of points equidistant [#permalink] ### Show Tags 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 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 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$\$.

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Re: What is the equation that represents the locus of points equidistant  [#permalink]

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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!
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What is the equation that represents the locus of points equidistant f  [#permalink]

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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
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Joined: 02 Aug 2009
Posts: 7108
Re: What is the equation that represents the locus of points equidistant f  [#permalink]

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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,

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
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Re: What is the equation that represents the locus of points equidistant  [#permalink]

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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

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Re: What is the equation that represents the locus of points equidistant  [#permalink]

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24 Sep 2018, 06:44
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Re: What is the equation that represents the locus of points equidistant &nbs [#permalink] 24 Sep 2018, 06:44
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