## Cartesian Plane Problem

Simplificatation, evaluation, linear equations, linear graphs, linear inequalities, basic word problems, etc.
macbluff619
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### Cartesian Plane Problem

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
Posts: 153
Joined: Sat Feb 28, 2009 8:53 pm

### Re: Cartesian Plane Problem

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.