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# In the rectangular co-ordinate systems, are the points (r,s)

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In the rectangular co-ordinate systems, are the points (r,s) [#permalink]

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22 Jul 2006, 15:00
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In the rectangular co-ordinate systems, are the points (r,s) & (u,v) equidistant from origin ?

1) r+s =1
2) u = 1-r and v = 1-s
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Re: GMATPrep: are points equidistnat? [#permalink]

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22 Jul 2006, 15:28
rkatl wrote:
In the rectangular co-ordinate systems, are the points (r,s) & (u,v) equidistant from origin ?

1) r+s =1
2) u = 1-r and v = 1-s

C . both togather are sufficient

need to prove u^2 + v^2 = r^2 + s^2

u = 1-r and v = 1-s
hence u^2 + v^2 = 1 + r^2 -2r + 1 +s ^2 -2s = r^2 + s ^2 + 2 - 2 (r+s) so u^2 + v^2 = r^2 + s^2 if r+s =1
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Re: GMATPrep: are points equidistnat? [#permalink]

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22 Jul 2006, 17:53
rkatl wrote:
In the rectangular co-ordinate systems, are the points (r,s) & (u,v) equidistant from origin ?

1) r+s =1
2) u = 1-r and v = 1-s

C.

distance of a point from the origin = sqrt(r^2 + x^2)

1. insufficient
2. dist of (u,v) = sqrt(r^2+s^2+2-2(r+s)) insuff

substituting r+s=1, we can prove the 2 expressions to be equal
Re: GMATPrep: are points equidistnat?   [#permalink] 22 Jul 2006, 17:53
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