${\left|AB\right|}^2+{\left|BS\right|}^2={\left|AS\right|}^2$
${\left(3\sqrt{5}\right)}^2+{\left(\sqrt{5}\right)}^2={\left|AS\right|}^2$
$45+5={\left|AS\right|}^2$
$\left|AS\right|=\sqrt{50}=\sqrt{25\cdot 2}=5\sqrt{2}$

$A\left(1,2\right)$, $S\left(x,x+1\right)$, $\left|AS\right|=5\sqrt{2}$
$\sqrt{{\left(x-1\right)}^2+{\left(x+1-2\right)}^2}=5\sqrt{2}|({)}^2$
${\left(x-1\right)}^2+{\left(x-1\right)}^2=50$
$2{\left(x-1\right)}^2=50$
${\left(x-1\right)}^2=25|\sqrt{}$
$\left|x-1\right|=5$
$x-1=5\vee x-1=-5$
$x=6x=-4$

• Dla $x=6$ mamy $y=6+1=7$
• Dla $x=-4$ mamy $y=-4+1=-3$              

Odp.: $C\left(-4,-3\right)$ lub $C\left(6,7\right)$