[Anu Radha]

L_2 has five lattice points.

Since the coordinates are integers, we can talk about whether they're odd or even.

Now, the coordinates of the midpoint of two points (x,y) and (z,u) are [(x+z)/2, (y+u)/2]

So, for the midpoint also to be a lattice point, x+z and y+u should be even.

Also notice that: odd+odd and even+even both give an even number

But, we can always find two distinct numbers x and z belonging to points in L_2 such that their sum is even (all odd, 1 even 2 odd, 2 even 3 odd, 3 even 2 odd, 4 even 1 odd or all even), so that their sum is even, and the same is the case for y and u.

(Note: this is true because all x,y,z,u are all integers)

So we can say that there are always two distinct points belonging to L_2 such that their midpoint is also a lattice point, not necessarily belonging to L_2.

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