The quadrilateral is a square
<h3>What are quadrilaterals?</h3>
Quadrilaterals are polygons, that have four sides and four corners
The coordinates are given as:
- A = (3, 5)
- B = (5, 2)
- C = (8, 4)
- D = (6, 7)
Start by calculating the adjacent side lengths using:
![d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}](https://tex.z-dn.net/?f=d%20%3D%20%5Csqrt%7B%28x_2%20-%20x_1%29%5E2%20%2B%20%28y_2%20-%20y_1%29%5E2%7D)
So, we have:
![AB = \sqrt{(3- 5)^2 + (5- 2)^2}](https://tex.z-dn.net/?f=AB%20%3D%20%5Csqrt%7B%283-%205%29%5E2%20%2B%20%285-%202%29%5E2%7D)
![AB = \sqrt{13}](https://tex.z-dn.net/?f=AB%20%3D%20%5Csqrt%7B13%7D)
![BC = \sqrt{(8- 5)^2 + (4- 2)^2}](https://tex.z-dn.net/?f=BC%20%3D%20%5Csqrt%7B%288-%205%29%5E2%20%2B%20%284-%202%29%5E2%7D)
![BC = \sqrt{13}](https://tex.z-dn.net/?f=BC%20%3D%20%5Csqrt%7B13%7D)
The side lengths are equal.
Hence, the quadrilateral is a square
Read more about quadrilaterals at:
brainly.com/question/5715879