Missing Point of a Parallelogram | Problem of the day

In parallelogram ABCD as opposite sides are parallel, compare triangles ABC and CDA. In these triangles AC = CA (common sides). Also ∠BAC =∠DCA (alternate interior angles), and ∠BCA = ∠DAC (alternate interior angles). Hence by the ASA criterion, both the triangles are congruent and the corresponding sides are equal. Therefore we have AB = CD, and BC = AD.

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[raviagrawal]

Why can't we use midpoint theorem to calculate D.
x4 = x1 + x3 - x2;
x5 = x2 + x3 - x1;
x6 = x1 + x2 - x3;
and similarly for their y-coordinates.
and the we will compare P4, P5 and P6 lexicographically.