Prove that the quadrilateral ABCD is a rectangle, find its area if A (15; 3), B (19; 5), C (17; 9) and D (13; 7).

Let us prove that this is a rectangle. Let us prove that the vector AB is parallel to the vector CD:

(AB) = (19 – 15; 5 – 3).

(AB) = (4; 2).

(CD) = (13 – 17; 7 – 9).

(CD) = (- 4; – 2).

(4/2) = ((- 4) / (- 2)).

We can argue that AB is parallel to CD.

Let’s find the length of vectors AB and CD:

| AB | = √ (16 + 4) = √20.

| CD | = √ (16 + 4) = √20.

Since the vectors are parallel and of the length are equal, it can be argued that this quadrilateral is a rectangle.

Find the area of the rectangle:

S = AB * CD = √20 * √20 = 20.

Answer: proven; twenty.