In this paper, we deal with the question: under what conditions n distinct points P_i(x_i,y_i) (i=1,...,n) provided x₁<...<x_n form a convex polygon? One of the main findings of the paper can be stated as follows: Let P₁(x₁,y₁),..., P_n(x_n,y_n) be n distinct points (n≥3) with x₁<...<x_n. Then \overline{P₁P₂},...,\overline{P_nP₁} form a convex n-gon lying in the half-space
\underline{H} = {(x,y)| x∈ℝ and y≤y₁ + [(x-x₁)/(x_n-x₁)](y_n-y₁)} ⊆ ℝ²
if and only if the following inequality holds
(y_i-y_i-1)/(x_i-x_i-1) ≤ (y_i+1-y_i)/(x_i+1-x_i) for all i∈{2,...,n−1}.
Based on this result, we establish a connection between the property of sequential convexity and convex polygon. We show that in a plane if any n points are scattered in such a way that their horizontal and vertical distances preserve some specific monotonic properties, then those points form a 2-dimensional convex polytope.