Question 13768
The idea is this: the points that are a distance of 2 from the origin forms a circle with radius 2 around the origin. The equation for that circle around the origin is {{{ x^2 + y^2 = 4}}} because the squares of the two sides formed by the x and y coordinates add up to the square of the hypotenuse.
{{{drawing(300, 300, -5, 5, -5, 5,circle(0,0, 2), line(-5, 0, 5, 0), line(0, 5, 0, -5), line(-sqrt(2), sqrt(2), 0, 0), line(-sqrt(2), sqrt(2), -sqrt(2), 0), locate(-2, 1, y), locate(-.9, -.1, x), locate(-.7, 1.2, 2))}}}
In the given case, since the x and y are known to be equal, then you have {{{x^2 + x^2 = 4}}}
which means {{{ 2x^2 = 4}}} and {{{x^2=2}}}. So, {{{x=sqrt(2)}}}
Since the square root can be plus or minus, the only question remaining is which is it? The answer lies in the second quadrant, which means the x value is negative and the y value is positive. So the coordinates of a point with the absolute values of the x and y values being equal that lies 2 from the origin are {{{ -sqrt(2)}}}  ,{{{ sqrt(2)}}}