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 r=1-s

if the 2 coordinates of one point have the same magnitude (absolute value), IN SOME ORDER, as the 2 coordinates of another point, then those 2 points are equidistant from the origin.**

there's no need to calculate the actual distances in this case.
since this is ridiculously awkward to state in words, here's an example: consider the point (4, 2). the statement above means that any other point with a "4" and a "2" as coordinates, no matter in what order or whether positive/negative, will be the same distance from the origin as is (4, 2) itself. in other words, (4, -2), (-4, 2), (-4, -2), (2, 4), (-2, 4), (2, -4), and (-2, -4) are all the same distance from the origin as is (4, 2).

two ways to approach this:
(1) algebra / substitution: statement 1 gives s = 1 - r. since u is also equal to 1 - r, we have s = u. also, v = 1 - s, so, substituting the above, v = 1 - (1 - r) --> v = r. since s = u and v = r, the above preliminary observation guarantees that (r, s) and (u, v) will be equidistant from the origin.

(2) plug in numbers: if you plug in random r's, the pattern will become ridiculously obvious very quickly. again, as i say in almost every strategy post, you should not hesitate to plug in numbers; if the algebra is not yielding to your smooth talk right away, go for the number plugging instead. try r = 0 --> this gives (r, s) = (0, 1) and (u, v) = (1, 0). equidistant. try r = 0.5 --> this gives (0.5, 0.5) and (0.5, 0.5). equidistant. try r = 10 --> this gives (10, -9) and (-9, 10). equidistant. try r = -3.4 --> this gives (-3.4, 4.4) and (4.4, -3.4). equidistant. you can see what's happening. (you should be convinced by the time you've done the first three, but, if you're not sure whether decimals would spoil the action, go ahead and plug in something like the fourth.) sufficient. answer = c