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

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 ($p$), 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.