If \[\mathbf{x}=\mathbf{2}.\overline{\mathbf{3}}-\mathbf{0}.\overline{\mathbf{9}},\] \[\mathbf{y}=\mathbf{2}\mathbf{.}\overline{\mathbf{5}}-\mathbf{0}.\overline{\mathbf{5}},\] then \[{{x}^{2}}+{{y}^{2}}-2xy\] is

• A. \[\frac{1}{4}\]
• B. \[\frac{1}{3}\]
• C. \[\frac{1}{2}\]
• D. \[\frac{1}{5}\]