Question

If three consecutive vertices of a parallelogram ABCD are A(1,-2), B(3,6) and C(5,10), find its fourth vertex D.

Answer 1

Let A(1,-2), B(3,6) and C(5,10) be the three vertices of a parallelogram ABCD and the fourth vertex be D(a,b).

Join AC and BD intersecting at O.

We know that the diagonals of a parallelogram bisect each other

Therefore, O is the midpoint of AC as well as BD.

Therefore, the fourth vertex is D(3,2).