How do you prove that the diagonals of a parallelogram bisect each other using coordinate geometry?

To prove that the diagonals of a parallelogram bisect each other using coordinate geometry, consider a parallelogram ABCD with vertices A(x1, y1), B(x2, y2), C(x3, y3), and D(x4, y4). The midpoint of diagonal AC is ((x1+x3)/2, (y1+y3)/2) and the midpoint of diagonal BD is ((x2+x4)/2, (y2+y4)/2). Since ABCD is a parallelogram, opposite sides are equal and parallel, leading to the conclusion that these midpoints are the same, thus proving that the diagonals bisect each other.

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