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

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24 Aug 2004, 14:27
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In the rectangular coordinate system, are the points (r,s) and (u,v) equidistant from the origin?

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

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24 Aug 2004, 18:06
1) Not sufficient. Does not tell anything anything about u and v

2) Not sufficient. Consider two cases, when (r,s) are at equal points such as (6,6) then (u,v) = (-5,-5). Their distance from the origin will then become 72^1/2 and 50^1/2.
Also consider the case when (r,s) are not equal, such as (-9,-10) then (u,v) = (10,11) and their distance are now 181^1/2 and 11^1/2.
But if (r,s)=(1/2,1/2) then (u,v) = (1/2,/1,2). Then their distance are equal.
So we don't know if they are equidistant from the origin without knowing more about r and s.

3) Use both.
Then (u,v) = (1-r, 1-s)= (1-1+s, 1-s) = (s,1-s)
(r,s) = (1-s, s)

Now calculating their distance from the origin, we get [s^2+(1-s)^2]^1/2 for both points. So using both equation are sufficient.

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