Question

What is the perimeter of the rectangle with the following vertices: (5,2), (-5,2) and (5,-3)?

Answer 1

Let the vertices of the rectangle are A = (5, 2), B = (-5, 2), C = (-5, -3) and D = (5, -3).

Distance between two points (x₁, y₁) and (x₂, y₂) formula : d = √[(x₂ - x₁)² + (y₂ - y₁)²].

 

A = (x₁, y₁) = (5, 2) and B = (x₂, y₂) = (-5, 2)

AB = √[{(-5) - (5)}² + {(2) - (2)}²] = 10

 

B = (x₁, y₁) = (-5, 2) and C = (x₂, y₂) = (-5, -3)

BC = √[{(-5) - (-5)}² + {(-3) - (2)}²] = 5

 

C = (x₁, y₁) = (-5, -3) and D = (x₂, y₂) = (5, -3)

CD = √[{(5) - (-5)}² + {(-3) - (-3)}²] = 10

 

D = (x₁, y₁) = (5, -3) and A = (x₂, y₂) = (5, 2)

DA = √[{(5) - (5)}² + {(2) - (-3)}²] = 5

 

Perimeter of the rectangle = AB + BC + CD + DA = 10 + 5 + 10 + 5 = 30 units.