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

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Manager
Joined: 13 Dec 2005
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In the rectangular coordinate system, are the points (r,s) [#permalink]  04 Jan 2006, 18:00
In the rectangular coordinate system, are the points (r,s) and (u,v) equidistant from the origin?

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

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
EACH statement ALONE is sufficient.
Statements (1) and (2) TOGETHER are NOT SUFFICIENT
Senior Manager
Joined: 08 Sep 2004
Posts: 258
Location: New York City, USA
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For (r,s) to be equidistance from origin as (u,v) -
r^2 + s^2 = u^2 + v^2

stmt1: r+s = 1. Does not say anything about (u,v). Not sufficient.

stmt2: u=1-r and v=1-s
u^2 + v^2 = 1 + r^2 - 2r + 1 + s^2 - 2s
= 2 - 2(r+s) + r^2 + s^2. Not suffcient.

Combining 1 & 2:

r^2 + s^2 = u^2 + v^2

Ans: C

- Vipin
Senior Manager
Joined: 14 Apr 2005
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Location: India, Chennai
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Re: Coordinate Geometry PowerPrep [#permalink]  04 Jan 2006, 23:08
ellisje22 wrote:
In the rectangular coordinate system, are the points (r,s) and (u,v) equidistant from the origin?

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

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
EACH statement ALONE is sufficient.
Statements (1) and (2) TOGETHER are NOT SUFFICIENT

The distance between (0,0) and (r,s) should be same as distance between (0,0) and (u,v)
Distance between (r,s) and (0,0) = sqrt(r^2+S^2)
Distance between (u,v) and (0,0) = sqrt(u^2+V^2)

Stmt 1 is obviously not suff.
From stmt 2 we get sqrt(2+r^2+s^2-2(r+s)) not suff.
Combing we get Sqrt(r^2+s^2) = SQRT(R^2+S^2)
Hence Suff. So C.
Director
Joined: 04 Oct 2005
Posts: 587
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I got C by plugging in values..but it took a long time 5 min
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