If A(2, 2), B(2, -2), C(-2, -2) and D(-2, 2)  are four points on the coordinate plane, do they form square ABCD?

Yes, the points A(2, 2), B(2, -2), C(-2, -2) and D(-2, 2) form a square ABCD. Here's why:

Step 1: Calculate the distances between the points. The distance between two points (x1, y1) and (x2, y2) on a coordinate plane is given by the formula √[(x2-x1)² + (y2-y1)²].

Using this formula, we find that: AB = √[(2-2)² + (-2-2)²] = 4 BC = √[(-2-2)² + (-2+2)²] = 4 CD = √[(-2+2)² + (2+2)²] = 4 DA = √[(2+2)² + (2-2)²] = 4

Step 2: Check if all sides are equal. Since AB = BC = CD = DA, all sides of the quadrilateral are equal.

Step 3: Calculate the diagonals. The diagonals of a square are equal. So, we calculate AC and BD. AC = √[(-2-2)² + (-2-2)²] = √32 BD = √[(2+2)² + (2+2)²] = √32

Step 4: Check if the diagonals are equal. Since AC = BD, the diagonals of the quadrilateral are equal.

Since all sides are equal and the diagonals are equal, ABCD is a square.