x + y = 0
y = -x
Sub this into the first equation
-x = x^2
x^2 + x = 0
x ( x + 1) = 0
Set both factors to 0 and solve for x
x = 0 and x = -1
When x = 0 y = 0
When x = -1 , y = 1
(0,0) and (-1, 1)
Distance between these = sqrt [ (-1)^2 + 1^2 ] = sqrt (2)