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
The answer in the book says C, but I don't know why the answer isn't B. Please explain. I can't seem to find a number that would make the points equidistant from the origin in B.
We are looking for whether the (r,s) and (u,v) share the same x-plane, y-plane or diagonal but equal distance.
- if same x-plane, then r = u and v = -s
- if same y-plane, then s = v and u = -r
- if diagonally, then (u,v) = (-s, -r)
Statement (1) alone gives us r + s = 1. Rearrange this to r = 1 - s. We are not given what (u,v). Not sufficient. Eliminate A and D.
Statement (2) alone gives us u = 1 - r and v = 1 - s. Replace (u,v) with (1-r, 1-s). Plot this with (r,s) from stimulus. Not sufficient. Why? Because the vital clue is "rectangular coordinate system
". As explained above, the coordinates must be on same x-plane, y-plane or diagonal but equal distance. Eliminate B.
Both Statement (1) and (2) together. Recall in Statement (1), we rearrange to r = 1 - s. Replace in (r,s) will give you (1-s,s). In Statement (2), we have the replacement of (u,v), which is (1-r,1-s).
Now replace r = 1-s in (1-r). You get (1-(1-s)), equals to 1-1+s equals s. Thus, (1-r,1-s) becomes (s,1-s).
We now have (1-s,s) and (s, 1-s) which show that both coordinates are equal distance but opposite of each other. Replace s with any value and you get a diagonal line between the coordinates and equidistance. Eliminate E.
Jimmy Low, Frankfurt, Germany
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