Question

Rectangle ABCD has vertices at A(-1,1), B(2,1), C(2,-5), and D(-1,-5). What is the perimeter of rectangle

Answer 1

The perimeter of the rectangle is 18 units.

Explanation:

The image included below presents the location of the points on the Cartesian plane. From Geometry we get that the perimeter (
`p`), dimensionless, of the rectangle is the sum of its four sides. That is to say:

`p = AB+BC+CD+DA` (1)

Where
`AB`,
`BC`,
`CD` and
`DA` 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)}`

`AB = 3`

`BC = \sqrt{(2-2)^(2)+[(-5)-1]^(2)}`

`BC = 6`

`CD = \sqrt{(-1-2)^(2)+(5-5)^(2)}`

`CD = 3`

`DA = \sqrt{(-1-1)^(2)+[1-(-5)]^(2)}`

`DA = 6`

And the perimeter of the rectangle is:

`p = 3+6+3+6`

`p = 18`

The perimeter of the rectangle is 18 units.