Find the perimeter and area of the square with side AB, if A (-3, 7); B (2, 3) The unit segment is 1 cm.

We have a square for which the coordinates of two neighboring vertices are known: A (-3; 7) and B (2; 3).

Find the perimeter and area of the square.

Points A and B are adjacent, which means that segment AB is a side of the square. Let’s find the size of the segment.

| AB | = ((2 + 3) ^ 2 + (3 – 7) ^ 2) ^ (1/2);

| AB | = (25 + 16) ^ (1/2);

| AB | = 41 ^ (1/2) cm.

The perimeter of a square is the size of the side of the square multiplied by 4:

P = 4 * | AB | = 4 * 41 ^ (1/2).

The area of the square is the square of the size of the side of the square:

S = | AB | ^ 2 = 41 cm².