In the rectangular coordinate system, are (r,s) and (u,v)

Question

In the rectangular coordinate system, are (r,s) and (u,v) equidistant from the origin?

(1) r+s=1
(2) u=1-r and v=1-s

popew626 · Answer

Tough DS. 

I'm going with C.

1 and 2 are obviously insufficient because they give info about each set of numbers seperately.

using the distance formula you can get the numbers to equal each other since you want both the same distance from 0. 

r^2 + s^2 = u^2 + v^2

from 2, 

u^2= (1-r)^2 and v^2= (1-s)^2

plug and chug and you get

r^2 + s^2 = u^2 + v^2

HIMALAYA · Answer

C. from i, r+s=1

from ii, u^2+v^2=(1-r)^2+(1-s)^2=2-2(r+s)+r^2+s^2

from i and ii, u^2+v^2=(1-r)^2+(1-s)^2
=2-2(r+s)+r^2+s^2
=r^2+s^2

vikramm · Answer

Yep. Got C too. Same reasoning as above.

macca · Answer

1, is insuff, no informatin about u,v

2,
we want to show that 

u^2 + v^2 = r^2 + s^2

So, substitue the values of u, and v
(1-r)^2 + (1-s)^2 = 2+r^2 + s^2 -2(r+s)

but we don't know what r+s is.

Combine 1 and 2, we'll get
(1-r)^2 + (1-s)^2 = 2+r^2 + s^2 -2(r+s) = r^2 +s^2

Therefore -> C it is.

In the rectangular coordinate system, are (r,s) and (u,v)

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