Question

In a plane, there are two families of lines $y=x+k,y=-x+k,$ where $k\in \{0,1,2,3,4\}$. The number of squares with diagonal of length $2$ units formed by the lines, is

Answer 1

Consider the lines $L_1,L_3$.
The lines $L_1,L_3$ form square with diagonal of length $2$ unit with lines $M_1,M_3$ and $M_2,M_4$ and $M_3,M_5$
So, for $L_1,L_3$, the number of such squares is $3$

As there are $3$ choices $((L_1,L_3),(L_2,L_4)(L_3,L_5))$ for the family $y=x+k$,
the total number of such squares is $3\times 3=9$