Respuesta :
Answer
Perimeter = 20 units.
Area = 25 square units.
Explanation
We are told to find the perimeter and area of the figure given by the coordinates K, L M and N. To do that, we need to obtain the lengths of each side of the figure.
The distance between two points with the coordinates (x₁, y₁) and (x₂, y₂) is given as
d = √[(x₂ - x₁)² + (y₂ - y₁)²]
For KL
(x₁, y₁) and (x₂, y₂) is K (-1, 1) and L (3, 4) respectively
x₁ = -1
y₁ = 1
x₂ = 3
y₂ = 4
d = √[(3 - (-1))² + (4 - 1)²]
d = √[(4)² + (3)²]
d = √(25)
d = 5
For LM
(x₁, y₁) and (x₂, y₂) is L (3, 4) and M (6, 0) respectively
x₁ = 3
y₁ = 4
x₂ = 6
y₂ = 0
d = √[(6 - 3)² + (0 - 4)²]
d = √[(3)² + (-4)²]
d = √(25)
d = 5
For MN
(x₁, y₁) and (x₂, y₂) is M (6, 0) and N (2, -3) respectively
x₁ = 6
y₁ = 0
x₂ = 2
y₂ = -3
d = √[(2 - 6)² + (-3 - 0)²]
d = √[(-4)² + (-3)²]
d = √(25)
d = 5
For NK
(x₁, y₁) and (x₂, y₂) is N (2, -3) and K (-1, 1) respectively
x₁ = 2
y₁ = -3
x₂ = -1
y₂ = 1
d = √[(-1 - 2)² + (1 - (-3))²]
d = √[(-3)² + (4)²]
d = √(25)
d = 5
We can see that the length of all the sides is the same. This figure is a square.
Perimeter = 4L = 4 (5) = 20 units
Area = L² = 5² = 25 square units.
Hope this Helps!!!
