Find the area of a rectangle with vertices at the points: A (-1; 4); B (2; 4); C (2; -1); D (-1; -1).

1. The coordinates of the vertices of the rectangle ABCD are given:

A (-1; 4);
B (2; 4);
C (2; -1);
D (-1; -1).
It is required to find its area.

2. As you can see, the sides AB and CD lie respectively on the straight lines y = 4 and y = -1, parallel to the abscissa axis, and the sides AD and BC, respectively, on the straight lines x = -1 and x = 2, parallel to the ordinate axis. Hence:

AD = y (A) – y (D) = 4 + 1 = 5;

AB = x (B) – x (A) = 2 + 1 = 3.

3. The area of the rectangle is equal to the product of the adjacent sides:

S = AD * AB = 5 * 3 = 15.

Answer. The area of the rectangle is 15.