Answer:
The perimeter of the rectangle is 18 units.
Step-by-step explanation:
The image included below presents the location of the points on the Cartesian plane. From Geometry we get that the perimeter (
), dimensionless, of the rectangle is the sum of its four sides. That is to say:
(1)
Where
,
,
and
are the sides of the rectangle, dimensionless.
Each side value is found by means of the Pythagorean Theorem:
![AB = \sqrt{[2-(-1)]^{2}+(1-1)^{2}}](https://tex.z-dn.net/?f=AB%20%3D%20%5Csqrt%7B%5B2-%28-1%29%5D%5E%7B2%7D%2B%281-1%29%5E%7B2%7D%7D)

![BC = \sqrt{(2-2)^{2}+[(-5)-1]^{2}}](https://tex.z-dn.net/?f=BC%20%3D%20%5Csqrt%7B%282-2%29%5E%7B2%7D%2B%5B%28-5%29-1%5D%5E%7B2%7D%7D)



![DA = \sqrt{(-1-1)^{2}+[1-(-5)]^{2}}](https://tex.z-dn.net/?f=DA%20%3D%20%5Csqrt%7B%28-1-1%29%5E%7B2%7D%2B%5B1-%28-5%29%5D%5E%7B2%7D%7D)

And the perimeter of the rectangle is:


The perimeter of the rectangle is 18 units.