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24 Jun 2008, 03:20
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B
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Difficulty:
65%
(hard)
Question Stats:
58% (02:20) correct
42%
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wrong
based on 256
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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
(A) 4x+y=20
(B) y+4x=10
(C) 4y+x=10
(D) y+2x=20
(E) x+4y=40
12 May 2016, 20:40
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ruchi857
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
24 Jun 2008, 03:35
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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.
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.
