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Identity the area and perimeter of the figure. K (-1,1), L (3,4), M (6,0), N (2,-3).

User Artahian
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Answer

Perimeter = 20 units.

Area = 25 square units.

Step-by-step 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!!!

User Zzaponka
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