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Solution: Valid Square

Explore how to verify if four given points in 2D space form a valid square by calculating squared distances and comparing side and diagonal lengths. Understand the geometric properties that define a square and apply an efficient algorithm to confirm the shape using these principles.

Statement

Given the coordinates of four points P1P_1, P2P_2, P3P_3, and P4P_4 in 2D space, determine if these points form a square.

Each point PiP_i is represented as [xi, yi][x_i,\space y_i] ...