Answer
$\large(\frac{\sqrt{2}}{2},-\frac{\sqrt{2}}{2}), (-\frac{\sqrt{2}}{2},\frac{\sqrt{2}}{2})$
Work Step by Step
Plugging in $y =-x$ in the equation $x^2+y^2 =1$
$$x^2+(-x)^2=1\\2x^2=1\\x^2=\frac{1}{2}$$
$$\therefore x=\pm \frac{\sqrt{2}}{2}$$
$$\therefore y=-x = \mp \frac{\sqrt{2}}{2}$$
The coordinates of the points of intersection are $\large(\frac{\sqrt{2}}{2},-\frac{\sqrt{2}}{2})$ and $\large(-\frac{\sqrt{2}}{2},\frac{\sqrt{2}}{2})$.
