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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 01 May 2008, 10:29
In the rectangular coordinate system, are the points (r,s) and (u,v) equidistance from the origin ?



1.r+s =1

2. u = 1-r and v=1-s


Please provide explaination
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Re: xy coordinate [#permalink] New post 01 May 2008, 10:54
alimad wrote:
In the rectangular coordinate system, are the points (r,s) and (u,v) equidistance from the origin ?



1.r+s =1

2. u = 1-r and v=1-s


Please provide explaination

(1) Only gives us information about r and s, u and v could be anything. INSUFFICIENT, eliminate AD.
(2) Plug in.
(r,s)=(0,0), (-1,-1), (1,1), (1,0), (0,1).
(u,v)=(1,1), (2,2), (0,0), (0,1), (1,0).
Equidistant from (0,0)? No, no, no, yes, yes.
INSUFFICIENT, eliminate B.

Now go back to (2) and look at all the (r,s) that resulted in (u,v) being equidistant from the origin. All r+s=1 worked, so you know that (1)+(2) is SUFFICIENT, eliminate E.

Answer: C.
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Re: xy coordinate [#permalink] New post 01 May 2008, 11:00
Statement 1:
Tells us only above r, and s and nothing about u & v so insufficient. Moreover r, & s can take any value (+ve, -ve, or even 0). Only restriction is their sum should be 1.

Statement 2:
u = 1-r and v=1-s => u+r = 1, v+s = 1
say u = v = 0.9 and r = s = 0.1.
Although equation is satisfied but (0.9, 0.9) is not at same distance from origin as (0.1, 0.1)

Combining both statements:
We have u+r = 1, v+s = 1, and r+s = 1
Add first two equation we have u+v+r+s = 2 => u+v = 1
Only possible way to satisfy this equation is u=v=r=s=0.5

So answer C.
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Re: xy coordinate [#permalink] New post 01 May 2008, 13:00
alimad wrote:
In the rectangular coordinate system, are the points (r,s) and (u,v) equidistance from the origin ?



1.r+s =1

2. u = 1-r and v=1-s


Please provide explaination


C

Using distance formula, you are looking to answer the question:
Is sqrt(r^2 + s^2) = sqrt(u^2 + v^2) ?
which is same as
Is r^2 + s^2 = u^2 + v^2 ?

(1) INSUFFICIENT, no u or v information

(2) Plug this back into
u^2 + v^2 = 1 - 2r + r^2 + 1 - 2s + s^2 = 2 - 2(r+s) + r^2 + s^2
Only true when r+s = 1
INSUFFICIENT

Using both, r+s=1, the question is answered.
SUFFICIENT
Re: xy coordinate   [#permalink] 01 May 2008, 13:00
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