Square ABCD has vertices at A(-1,3) B(0,7) C(4,6) and D(3,2). How many units is the perimeter of square ABCD

16.492422502 units or 4√17 units

Step-by-step explanation:

The Perimeter of a Square can be defined as the Addition of it's 4 sides or the Multiplication of 4 and one of its sides.

This means,

The perimeter of square = a + b + c + d

or

4 × any of the sides because the sides of a square are equal to one another.

In the above question, we are given vertices at A(-1,3) B(0,7) C(4,6) and D(3,2)

The formula to solve for this is

√(x2 - x1)² + (y2 - y1)² when you have vertices: (x1 , y1 ) and (x2 , y2)

For Side AB: A(-1,3), B(0,7)

= √(x2 - x1)² + (y2 - y1)²

= √(0- (-1))² + (7 - 3)² = √1² + 4² = √1 + 16 = √17

For Side BC: B(0,7), C(4,6)

√(x2 - x1)² + (y2 - y1)²

= √(4 - 0)² + (6 - 7)² = √4² + 1² = √16 + 1 = √17

For Side AD : A(-1,3), D(3,2)

= √(x2 - x1)² + (y2 - y1)²

= √(3- (-1))² + (2 - 3)² = √4² + (-1)² = √16 + 1= √17

For Side CD: C(4,6), D(3,2)

= √(x2 - x1)² + (y2 - y1)²

= √(3 - 4)² + (6 - 2)² = √-1² + 4² = √1 + 16 = √17

From the above calculations we can side that sides AB = BC = AC = CD

Hence the perimeter of square ABCD can be calculated as 4 × √17 or √17 + √17 + √17 + √17

= 16.492422502 units or 4√17 units