By distance formula: \(d = \sqrt{(\cos {A} - \sin {A})^2 +(-\sin {A} -\cos {A})^2}\)

\(d^2 = \cos^2 {A} -2\cos {A} \sin {A} + \sin^2 {A} + \sin {A} + 2 \sin {A} \cos {A} + \cos^2 {A} \)

\(d^2 = 2\cos^2 + 2\sin^2 {A}\)

\(d = \sqrt{2} (1)\)

\(d = \sqrt{2}\), Answer