Final answer:
The perimeter of square ABCD is calculated using the distance formula for the length of one side, which is found to be 2√13. Multiplying this by 4 (since all sides of a square are equal), we find the perimeter to be 8√13.
Step-by-step explanation:
To find the perimeter of square ABCD, we must first calculate the length of one of its sides. Since a square has all sides of equal length, we can find the length of one side and then multiply that by 4 to get the perimeter. Let's use vertices A and B to calculate the length of side AB.
We calculate the length of a side of a square by using the distance formula for two points in a plane, which is √((x2-x1)² + (y2-y1)²). In this case for points A(-2,1) and B(2,7), the length of AB is √((2-(-2))² + (7-1)²) = √((4)² + (6)²) = √(52) which simplifies to √(4²³13), resulting in a side length of 2√13.
Now, to find the perimeter of square ABCD, we multiply this length by 4: Perimeter = 4(2√13) = 8√13.