Cartesian Plane Problem

[macbluff619]

The following question is in my textbook Algebra and Trigonometry, Carl Stitz, Ph.D, Jeff Zeager, Ph.D. a free textbook I found online.

Find all of the points of the form (x, -x) which are 1 unit from the origin.

The answer is given as
(sqrt(2)/2, -sqrt(2)/2), (-sqrt(2)/2, (sqrt(2)/2)

I understand the other questions but I'm totally lost on how this answer was obtained. It's found in a chapter on If someone could work the problem so I can see how it is done, I would really appreciate it.

[FWT]

Find all of the points of the form (x, -x) which are 1 unit from the origin.

The answer is given as
(sqrt(2)/2, -sqrt(2)/2), (-sqrt(2)/2, (sqrt(2)/2)

I understand the other questions but I'm totally lost on how this answer was obtained.

Plug it into the distance formula and see what happens:

1 = sqrt[(x - 0)^2 + (-x - 0)^2]
1 = sqrt[x^2 + x^2]
1 = sqrt[2x^2]
1 = 2x^2

yada, yada. Solve for x and backsolve for y.