By the Pythogoras theorem:

\(\displaystyle{x}^{{{2}}}+{y}^{{{2}}}={1}\)

so, if x=y, we will have:

\(\displaystyle{x}^{{{2}}}+{y}^{{{2}}}={1}\)

\(\displaystyle{2}{y}^{{{2}}}={1}\)

\(\displaystyle{y}^{{{2}}}={\frac{{{1}}}{{{2}}}}\)

\(\displaystyle{y}=\sqrt{{{\frac{{{1}}}{{{2}}}}}}={\frac{{\sqrt{{{2}}}}}{{{2}}}}\)

\(\displaystyle{x}^{{{2}}}+{y}^{{{2}}}={1}\)

so, if x=y, we will have:

\(\displaystyle{x}^{{{2}}}+{y}^{{{2}}}={1}\)

\(\displaystyle{2}{y}^{{{2}}}={1}\)

\(\displaystyle{y}^{{{2}}}={\frac{{{1}}}{{{2}}}}\)

\(\displaystyle{y}=\sqrt{{{\frac{{{1}}}{{{2}}}}}}={\frac{{\sqrt{{{2}}}}}{{{2}}}}\)