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

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Manager
Joined: 02 May 2008
Posts: 80
In the rectangular coordinate system are the points (r,s)  [#permalink]

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15 Jul 2008, 09:40
In the rectangular coordinate system are the points (r,s) ans (u,v) equidistant from the origin?
1) r+s=1
2) u=1-r and v=1-s

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Current Student
Joined: 04 Jan 2005
Posts: 281
Location: Milan
Schools: Wharton, LBS, UChicago, Kellogg MMM (Donald Jacobs Scholarship), Stanford, HBS

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15 Jul 2008, 09:54
1. does not tell nothing about (u,v)

2. A(1,1) then B(0,0) obviously insuff

Combined: the two points coincide, suff
Manager
Joined: 27 May 2008
Posts: 192

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15 Jul 2008, 10:04

if they are equi distance

then r^2 + s^2 = u^2+v2

1) r+s=1 == INSUFF

2) u=1-r v=1-s
substitue in above equation you will get r+s = 1

so combing with 1, we can say both are equi distance
Intern
Joined: 26 Jul 2007
Posts: 32

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16 Jul 2008, 05:17
selvae wrote:

if they are equi distance

then r^2 + s^2 = u^2+v2

1) r+s=1 == INSUFF

2) u=1-r v=1-s
substitue in above equation you will get r+s = 1

so combing with 1, we can say both are equi distance

Hello what i don't understand is how you say r^2+s^2=u^2+v^2.
I know we have r+s=1 => r^2+s^2=1-2*s*r and u+v=1 => u^2+v^2=1-2*u*v
Since you conclude r^2+s^2=u^2+v^2 you must have concluded that r*s=u*v which i'm not sure about even when you combine the two assumptions!!
I get E for this question.
VP
Joined: 17 Jun 2008
Posts: 1474

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16 Jul 2008, 07:02
Stmt1 : r + s = 1...hence r = 1-s or s = 1-r
Stmt2: u = 1-r = s and v = 1-s = r

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

Distance of (r,s) from origin = sqrt(r^2 + s^2)
and of (u,v) from origin = sqrt(u^2 + v^2).

Hence, C should be the answer.
Manager
Joined: 02 May 2008
Posts: 80

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16 Jul 2008, 08:17
Hi,
I found this Q in OG-11 ..

Poullo,
U can refer to Q no 140.

The explanation is very similar to what scthakur has put down, but uses a diff approach
dist (r,s) from the origin =sqrt(r^2+s^2)

dist(u,v) = sqrt(v^2+u^2)

using stmt 2
v^2+u^2 =(1-r)^2 + (1-s) ^2
= 1+ r^2 -2r + 1+ s^2 -2s
= 2- 2(r+s) +r^2+s^2

Now use stmt 1(r+1=1) in the above eq
v^2+u^2=2- 2(1) +r^2+s^2
=r^2+s^2
Intern
Joined: 26 Jul 2007
Posts: 32

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25 Jul 2008, 05:25
MamtaKrishnia wrote:
Hi,
I found this Q in OG-11 ..

Poullo,
U can refer to Q no 140.

The explanation is very similar to what scthakur has put down, but uses a diff approach
dist (r,s) from the origin =sqrt(r^2+s^2)

dist(u,v) = sqrt(v^2+u^2)

using stmt 2
v^2+u^2 =(1-r)^2 + (1-s) ^2
= 1+ r^2 -2r + 1+ s^2 -2s
= 2- 2(r+s) +r^2+s^2

Now use stmt 1(r+1=1) in the above eq
v^2+u^2=2- 2(1) +r^2+s^2
=r^2+s^2

Thanks u right i just was lazy in this one!

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This is not a quality discussion. It has been retired.

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Re: rectangular coordinate system &nbs [#permalink] 25 Jul 2008, 05:25
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# In the rectangular coordinate system are the points (r,s)

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