Final answer:
The perimeter of the triangle is 5 + 2√17 units.
Step-by-step explanation:
The perimeter of a triangle can be found by adding the lengths of all three sides. To find the lengths of the sides, we can use the distance formula:
d = √((x₂ - x₁)² + (y₂ - y₁)²)
Using the given coordinates, we can calculate the lengths of each side:
- Side 1: √((2 - (-1))² + (2 - (-2))²) = √(3² + 4²) = 5 units
- Side 2: √((1 - 2)² + (-2 - 2)²) = √((-1)² + (-4)²) = √(1 + 16) = √17 units
- Side 3: √((2 - 1)² + (2 - (-2))²) = √(1² + 4²) = √(1 + 16) = √17 units
Finally, we can find the perimeter by adding the lengths of all three sides: 5 units + √17 units + √17 units = 5 units + 2√17 units. Therefore, the perimeter of the triangle is 5 + 2√17 units.