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In a plane there are two families of lin...

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:

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The correct Answer is:
9
Each family has parallel lines having the distance between them as `1//sqrt(2)` unit. Both the families are perpendicular to each other. So, to form a square of diagonal 2 units, lines of alternate pair are to be chosen.
Both the families have three such pairs. So, the number of squares possible is `3 xx 3 =9.`
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