Rotated triangle

We must assume that the red line is between a vertex and it's transformed image. It is given that side $a$ is perpendicular to $a'$ . It is also given that $a$ , as well as $a'$ has a side length of 1. Using Pythagorean theorem, we can work the problem out (with $c$ as the red line): $1^2+1^2=c^2$ $\implies~2=c^2$ $\implies~c=\sqrt{2}$ $\sqrt{2}~\approx~\boxed{1.41}$