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# ds-coordinates

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VP
Joined: 17 Jun 2008
Posts: 1279

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18 Oct 2008, 21:52
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In a rectangular coordinate system ,are the points (r,s) and (u,v)
equidistant from origin?
1)r+s=1
2)u=1-r and v=1-s

Kindly HELP solving this since im not able to get to the answer !!!

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VP
Joined: 30 Jun 2008
Posts: 1004

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18 Oct 2008, 21:59
spriya wrote:
In a rectangular coordinate system ,are the points (r,s) and (u,v)
equidistant from origin?
1)r+s=1
2)u=1-r and v=1-s

Kindly HELP solving this since im not able to get to the answer !!!

Origin is (0,0). Distance between origin and (r,s) is SQRT(r² + s²) and Distance between origin and (u,v) is SQRT(u² + v²)

so we have to prove if SQRT(u² + v²) = SQRT(r² + s²)

Now (1) is insufficient since it provides us NO information reg u and v

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

distance from (0,0) and (u,v) is = SQRT(u² + v²)
= SQRT((1-r)² + (1-s)²)
= SQRT(1 + r²- 2r + 1 + s² - 2s)
= SQRT(2 -2(r+s) + r² + s²)

Now we are stuck here. 2 also insufficient.

Combining 1 and 2 we get -- SQRT(u² + v²) = SQRT(2 -2(r+s) + r² + s²)
from 1 we get r+s =1 on substituting this in the above equation we get SQRT(u² + v²) = SQRT(r² + s²)

Hence the answer must be C
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VP
Joined: 17 Jun 2008
Posts: 1279

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18 Oct 2008, 22:25
amitdgr wrote:
spriya wrote:
In a rectangular coordinate system ,are the points (r,s) and (u,v)
equidistant from origin?
1)r+s=1
2)u=1-r and v=1-s

Kindly HELP solving this since im not able to get to the answer !!!

Origin is (0,0). Distance between origin and (r,s) is SQRT(r² + s²) and Distance between origin and (u,v) is SQRT(u² + v²)

so we have to prove if SQRT(u² + v²) = SQRT(r² + s²)

Now (1) is insufficient since it provides us NO information reg u and v

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

distance from (0,0) and (u,v) is = SQRT(u² + v²)
= SQRT((1-r)² + (1-s)²)
= SQRT(1 + r²- 2r + 1 + s² - 2s)
= SQRT(2 -2(r+s) + r² + s²)

Now we are stuck here. 2 also insufficient.

Combining 1 and 2 we get -- SQRT(u² + v²) = SQRT(2 -2(r+s) + r² + s²)
from 1 we get r+s =1 on substituting this in the above equation we get SQRT(u² + v²) = SQRT(r² + s²)

Hence the answer must be C

Yes OA is C !!i just did not want to do so much of calculation !!so got this one wrong !!just guessed !!
Is there any simpler way to do this ,like which takes less time !!
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Its Now Or Never

Manager
Joined: 04 Sep 2008
Posts: 233
Location: Kolkata
Schools: La Martiniere for Boys

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21 Oct 2008, 03:49
There is a simpler way but its similar.

Now we need to prove that u^2 + v^2 = (1-r)^2 + (1-s)^2

RHS = 1-2r-2s + u^2 + s^2

Now we can only come to our desired result if (1-2r -2s) =0 or in other words r+s =0. This condition is given by A. So we have to combine A with B for our desired result. Hence C
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Thanks
rampuria

VP
Joined: 30 Jun 2008
Posts: 1004

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21 Oct 2008, 03:55
rampuria wrote:
There is a simpler way but its similar.

Now we need to prove that u^2 + v^2 = (1-r)^2 + (1-s)^2

RHS = 1-2r-2s + u^2 + s^2

Now we can only come to our desired result if (1-2r -2s) =0 or in other words r+s =0. This condition is given by A. So we have to combine A with B for our desired result. Hence C

I don't get the portion in red
_________________

"You have to find it. No one else can find it for you." - Bjorn Borg

Retired Moderator
Joined: 18 Jul 2008
Posts: 893

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21 Oct 2008, 11:59
try this:

1)r+s=1 NOT SUFFICIENT

2)u=1-r and v=1-s NOT SUFFICIENT

If using 1) + 2)

u=1-r
Can be written as: r= 1-u

v=1-s
Can be written as: s= 1-v

r+s = 2 - u - v
From 1) r+s= 1

1 = 2 - u - v
u+v =1

Both 1), 2) are giving the same value (both =1), thus, equidistant.

What do you guys think?
SVP
Joined: 07 Nov 2007
Posts: 1728
Location: New York

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21 Oct 2008, 13:26
1
spriya wrote:
In a rectangular coordinate system ,are the points (r,s) and (u,v)
equidistant from origin?
1)r+s=1
2)u=1-r and v=1-s

Kindly HELP solving this since im not able to get to the answer !!!

Here is simple way.

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

r+s=1=u+r --> s=u
r+s=1=v+s --> r=v

So (r,s) and(u,v) are same points.. so must be equidistant from origin.
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VP
Joined: 30 Jun 2008
Posts: 1004

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21 Oct 2008, 21:07
x2suresh wrote:
spriya wrote:
In a rectangular coordinate system ,are the points (r,s) and (u,v)
equidistant from origin?
1)r+s=1
2)u=1-r and v=1-s

Kindly HELP solving this since im not able to get to the answer !!!

Here is simple way.

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

r+s=1=u+r --> s=u
r+s=1=v+s --> r=v

So (r,s) and(u,v) are same points.. so must be equidistant from origin.

thats a really neat way of doing this problem

--== Message from GMAT Club Team ==--

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

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.

_________________

"You have to find it. No one else can find it for you." - Bjorn Borg

Re: ds-coordinates &nbs [#permalink] 21 Oct 2008, 21:07
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