The diagonals of a parallelogram bisect each other. Steps (a), (b), and (c) outline a pr...

The diagonals of a parallelogram bisect each other. Steps (a), (b), and (c) outline a proof of this theorem. (See Exercise 25 for a particular instance of this theorem.)

(a) In the parallelogram OABC shown in the figure, check that the coordinates of B must be (a + b, c). (b) Use the midpoint formula to calculate the midpoints of diagonals

(c) The two answers in part (b) are identical. This shows that the two diagonals do indeed bisect each other, as we wished to prove

Reference

(a) Sketch the parallelogram with vertices A(-7, -1), B(4, 3), C(7, 8), and D(-4, 4).

(b) Compute the midpoints of the diagonals and

(c) What conclusion can you draw from part (b)?