Given A = (–2, –1), B = (3, 0) and C = (1, –2)

Let the other vertex D = (x, y)

We know position vector of a point (x, y) is given by, where and are unit vectors in X and Y directions.

Let position vectors of points A, B, C and D be,, and respectively.

We also have.

Similarly and.

Recall the vector is given by

Similarly, the vector is given by

But, it is given that ABCD is a parallelogram.

(as the opposite sides are parallel and equal)

By comparing both sides, we get 1 – x = 5 and 2 + y = –1

⇒ x = 1 – 5 = –4

and y = –1 – 2 = –3

So, x = –4 and y = –3

Thus, vertex D of parallelogram ABCD = (–4, –3).