Consider the fourteen lines in the plane given by y=x+r, y=-x+r, where r 0,1,2,3,4,5,6 . The number of squares formed by these lines, whose sides are of length 2 , is :

Step-by-step solution

We have, y=x+r (i) and y=-x+r (ii) The given lines are perpendicular to each other. perpendicular distance = |r₁-r₂ | 2 = 2 r₁-r₂=2 The difference between the y -intercepts =2 This can happen for five combinations (0,2),(1,3),(2,4),(3,5),(4,6) The difference between the x -intercepts =2 This can happen for five combination the total number of squares =5 5=25