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

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In the rectangular coordinate system, are the points (r,s) [#permalink] New post 04 Jan 2006, 19:00
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
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 [#permalink] New post 04 Jan 2006, 19:28
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

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Re: Coordinate Geometry PowerPrep [#permalink] New post 05 Jan 2006, 00:08
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.
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 [#permalink] New post 07 Jan 2006, 00:49
I got C by plugging in values..but it took a long time 5 min
  [#permalink] 07 Jan 2006, 00:49
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