Here are the coordinates for eight points on the coordinate plane (q p 0): A (0, 0), B (p, 0), C (q, 0), D (p + q, 0), E (0, q), F (p, q), G (q, q), and H (p + q, q). Which four points, if any, are on the vertices of a parallelogram? plz help thx :)

Question

Here are the coordinates for eight points on the coordinate plane (q > p > 0): A (0, 0), B (p, 0), C (q, 0), D (p + q, 0), E (0, q), F (p, q), G (q, q), and H (p + q, q). Which four points, if any, are on the vertices of a parallelogram? plz help thx :)

amoodarya · Answer

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hint 
FOR BEING parallelogram
$$(X_A,Y_A)+(X_C,Y_C) =(X_B,Y_B)+(X_D,Y_D)$$