Calculate the perimeter and area of a rectangle if its three vertices are known: A (-3; 2), B (4; 2), C (4; -1).

Let’s find the length of the side AB. The distance between two points is determined as the root of the sum of the squares of the differences in the coordinates of the points:
AB = √ ((xb − xa) ² + (yb − ya) ²) = √ ((4 + 3) ² + (2 – 2) ²) = √49 = 7 cm.

Let’s find the length of the BC side:
ВС = √ ((xс − xb) ² + (yc − yb) ²) = √ ((4 – 4) ² + (-1 – 2) ²) = √9 = 3 cm.

Find the perimeter of the rectangle:
P = (AB + BC) * 2 = (7 + 3) * 2 = 20.

Find the area of the rectangle:
S = AB * BC = 7 * 3 = 21.

Answer: the perimeter of the rectangle ABCD is 20, and its area is 21.