Answer:
Perimeter = 22
Step-by-step explanation:
To find the perimeter, we will follow the steps below:
A = (-1,-1), B = (2,3), C = (5,3), D = (8,-1).
First, we will find the distance AB
A = (-1,-1), B = (2,3)
|AB| = √(x₂-x₁)²+(y₂-y₁)²
x₁ = -1 y₁=-1 x₂=2 y₂=3
we can now proceed to insert the values into the formula
|AB| = √(x₂-x₁)²+(y₂-y₁)²
= √(2+1)²+(3+1)²
= √(3)²+(4)²
= √9 + 16
=√25
= 5
|AB| = 5
Next, we will find the distance BC
B = (2,3), C = (5,3),
|BC| = √(x₂-x₁)²+(y₂-y₁)²
x₁ = 2 y₁=3 x₂=5 y₂=3
we can now proceed to insert the values into the formula
|BC| = √(x₂-x₁)²+(y₂-y₁)²
= √(5-2)²+(3-3)²
= √(3)²+(0)²
= √9 + 0
=√9
= 3
|BC|=3
Next, we will find the distance CD
C = (5,3), D = (8,-1).
|CD| = √(x₂-x₁)²+(y₂-y₁)²
x₁ = 5 y₁=3 x₂=8 y₂=-1
we can now proceed to insert the values into the formula
|CD| = √(x₂-x₁)²+(y₂-y₁)²
= √(8-5)²+(-1-3)²
= √(3)²+(-4)²
= √9 + 16
=√25
= 5
|CD|=5
Next, we will find the distance DA
D = (8,-1) A = (-1,-1)
|DA| = √(x₂-x₁)²+(y₂-y₁)²
x₁ = 8 y₁=-1 x₂=-1 y₂=-1
we can now proceed to insert the values into the formula
|DA| = √(x₂-x₁)²+(y₂-y₁)²
= √(-1-8)²+(-1+1)²
= √(-9)²+(0)²
= √81 + 0
=√81
= 9
|DA|=9
PERIMETER = |AB|+|BC|+|CD|+|DA|
=5 + 3+5 +9
=22
Perimeter = 22
