32. Parallelogram ABCD has vertices A(0,0), B(2,4), and C(10,4). Find the coordinates of D.

The fourth vertex is D(8, 0)

Step-by-step explanation:

Let A(0, 0), B(2, 4), and C(10, 4) be the three vertices of a parallelogram ABCD and let its fourth vertex be D(a, b).

Join AC and BD. Let AC and BD intersect at point O.

So, O would be the midpoint of AC as well as that of BD.

The midpoint of AC is:

The midpoint of BD is:

so

∵  

∵

Hence, the fourth vertex is D(8, 0)