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M10 - Q#27 - Coordinate Geometry

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Manager
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Joined: 16 Jul 2009
Posts: 247

Kudos [?]: 447 [0], given: 3

M10 - Q#27 - Coordinate Geometry [#permalink]

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New post 08 May 2010, 12:15
Is point A closer to point (1,2) than to point (2,1)?

1. Point A lies on the line y=x
2. Point A lies on the line y=-x

Please explain how is the OA:
[Reveal] Spoiler:
A

Kudos [?]: 447 [0], given: 3

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Joined: 20 Apr 2010
Posts: 151

Kudos [?]: 19 [0], given: 16

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Re: M10 - Q#27 - Coordinate Geometry [#permalink]

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New post 11 May 2010, 22:55
Distance d between any 2 points ( x,y ) and ( a,b ) is given as

d = \sqrt{( (x-a)^2 + (y-b)^2 )}

1. Point A lies on the line y=x
Lets take 2 points on line A i.e. ( 1,1 ) & (-1,-1) & by using above mentioned formula :
-------------------------- (1,2) ---------------------------(2,1)
Distance from ( 1,1 ) ---------- 1 ---------------------- 1
Distance from ( -1,-1 )-------------\sqrt{13}--------------- 13\sqrt{}

Therefore in both cases Point A is not closer but equidistant . So sufficient.

2. Point A lies on the line y=-x
Lets take 2 points on line A i.e. ( 1,-1 ) & (-1,1) & by using above mentioned formula :
------------------------------ (1,2)------------------------ (2,1)
Distance from ( 1,-1 ) ------------- 3 ---------------- \sqrt{5}
Distance from (-1,1 )---------- \sqrt{5}------------------- 3
Therefore first case its farther , second case its closer . so Not sufficient

Answer : A

I hope i was able to explain... sorry for improper style...

Kudos [?]: 19 [0], given: 16

Re: M10 - Q#27 - Coordinate Geometry   [#permalink] 11 May 2010, 22:55
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M10 - Q#27 - Coordinate Geometry

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