Let A(2, 3), B(5, 4), and C(3, 8) be three points in a coordinate plane. Find the coordinates of the point D such that the points A, B, C, and D form a parallelogram with
a. AB as one of the diagonals.
b. AC as one of the diagonals.
c. BC as one of the diagonals.
[Hint: Use Exercise 1.]
Exercise 1
Use coordinates to prove that the diagonals of a parallelogram bisect each other.
[Hint: Choose (0, 0) (a, 0), (b, c), and (a + b, c) as the vertices of a parallelogram.]
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