Find the minimum number of edges which will have its midpoint (of the line segment corresponding to that edge) as a lattice point .

If both x and y are integers, then the point P(x,y) is called a lattice point of the plane. Suppose Pi, 1 <= i <= 5, are five (different) lattice points. We form a complete graph using these 5 points and the unique straight line segments (edges) determined by the C(5,2) = 10 pairs of these points. For any given values of lattice points, the minimum number of edges which will have its midpoint (of the line segment corresponding to that edge) as a lattice point is:

(A) 1
(B) 2
(C) 3
(D) 4

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