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In the rectangular coordinate system, are the points (r,s)

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Senior Manager
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In the rectangular coordinate system, are the points (r,s) [#permalink] New post 27 Aug 2007, 08:02
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In the rectangular coordinate system, are the points (r,s) and (u,v) equidistant from the origin?

(1) r+s=1
(2) u=1-r and v=1-s
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Re: Another DS question [#permalink] New post 27 Aug 2007, 11:18
[quote="Vlad77"]In the rectangular coordinate system, are the points (r,s) and (u,v) equidistant from the origin?

(1) r+s=1
(2) u=1-r and v=1-s[/quote]

Distance from origin is sqrt(r^2+s^2) and sqrt(u^2+v^2) respectively.

St1: Insuff. Says nothing about u & v.

St2: From
u^2+v^2 = s^2+r^2 +2 -2(r+s)

Insuff. We do not know r+s? If r+s >1, then (u,v) closer. r+s<1, (r,s) closer.

St1+St2: Sufficient. Equidistant points.
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Re: Another DS question [#permalink] New post 27 Aug 2007, 14:58
Vlad77 wrote:
In the rectangular coordinate system, are the points (r,s) and (u,v) equidistant from the origin?

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


Use the distance formula D=sqrt of (x1-x2)^2+(y1-y2)^2

Use the D formula for both (r,s) and (u,v) for x2 and y2 for both equations use 0,0.

This gives you r^2+s^2=u^2+v^2

now looking at the stmnts. 1 is clearly not sufficient

2: doesnt give us everything we need either.

S1 and S2 give us enough to solve this out.

Ans C
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 [#permalink] New post 27 Aug 2007, 22:35
Thanks :-D
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Re: Another DS question [#permalink] New post 15 Sep 2007, 05:57
S1=> 1 - s = r
1 - r = s

From S2 => (u, v) = (1-r, 1-s)

Combining:
(u, v) = (1-r, 1-s)
(u,v) = (s, r)

(r, s) and (s, r) [(u, v)] are equidistance from the origin.
C
Re: Another DS question   [#permalink] 15 Sep 2007, 05:57
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