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

To be 1 unit from the origin, points must lie on the unit circle, or 
x^2+(-x)^2=1
x=+/- sqrt(2)
If the point is restricted to the form (x,-x), then
x=sqrt(2)  => P1=(sqrt(2),-sqrt(2))
x=-sqrt(2) => P2=(-sqrt(2),sqrt(2))

Therefore there are two such points.