Question

On a coordinate plane, square A B C D is shown. Point A is at (3, 4), point B is at (2, negative 2), point C is at (negative 4, negative 1), and point D is at (negative 3, 5). What is the perimeter of square ABCD? StartRoot 37 EndRoot units 4 StartRoot 37 EndRoot units 28 units 37 units

Answer 1

Answer:

4$\sqrt{37}$

Step-by-step explanation:

Since the figure is a square, find the length of 1 side and multiply by 4 for perimeter.

Calculate the length of AB using the distance formula.

AB = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = A(3, 4) and (x₂, y₂ ) = B(2, - 2)

AB = $\sqrt{(2-3)^2+(-2-4)^2}$

     = $\sqrt{(-1)^2+(-6)^2}$

     = $\sqrt{1+36}$

     = $\sqrt{37}$

Hence

perimeter = 4AB = 4$\sqrt{37}$