In a plane there are two families of lines `y=x+r, y=-x+r`, where `r in {0, 1, 2, 3, 4 }`. The number of squares of diagonals of length 2 formed by the lines is:

Options

A. 9
B. 16
C. `(3)/(2)*.^(4)C_(2)`
D. `5_(C_(2))+.^(3)P_(2)`

Answer

A, C

Explanation

There are two sets of five parallel lines at equal distance. Clearly, lines like `l_(1),l_(3),m_(1) and m_(3)` form a square whose diagonal's length is 2.

`therefore`Number of required squares`=3xx3=9=(3)/(2)*.^(4)C_(2)`
[`because` are `(l_(1),l_(2)),(l_(2),l_(4)) and (l_(3),l_(5))` for one set, etc.]