Request you to do a search before u post...

check out the link:
https://www.beatthegmat.com/coordinate-s ... 12489.html

girishbtg wrote:

Is r^2 + s^2 = u^2 + v^2?

[1] r + s = 1, this is insufficient.

[2] u = 1 - r and v = 1 - s, this makes r^2 + s^2 = 1 - 2 u + u^2 + 1 - 2 v + v^2 = u^2 + v^2, if and only if u + v = 1; who knows? Insufficient

Taken together

If r + s = 1, then u + v = 1 - r + 1 - s = 2 - (r + s) = 2 - 1 = 1, and then, [spoiler]r^2 + s^2 = u^2 + v^2. Sufficient


C[/spoiler]