The distance between the two points $A$ and $A ^ { \prime }$ which lie on $y = 2$ such that both the line segments $A B$ and $A ^ { \prime } B$ (where $B$ is the point $( 2,3 )$ ) subtend angle $\frac { \pi } { 4 }$ at the origin, is equal to\\
(1) 10\\
(2) $\frac { 48 } { 5 }$\\
(3) $\frac { 52 } { 5 }$\\
(4) 3