Answer:
9 + √41 units
Explanation:
To find the perimeter of triangle ABC, we need to calculate the lengths of its sides using the given coordinates.
The distance formula can be used to find the length between two points (x₁, y₁) and (x₂, y₂):
Distance = √((x₂ - x₁)² + (y₂ - y₁)²)
Let's calculate the lengths of the sides:
Side AB:
A(-1, 5) and B(4, 5)
Distance AB = √((4 - (-1))² + (5 - 5)²)
= √(5² + 0²)
= √25
= 5
Side BC:
B(4, 5) and C(-1, 1)
Distance BC = √((-1 - 4)² + (1 - 5)²)
= √((-5)² + (-4)²)
= √(25 + 16)
= √41
Side AC:
A(-1, 5) and C(-1, 1)
Distance AC = √((-1 - (-1))² + (1 - 5)²)
= √(0² + (-4)²)
= √16
= 4
Now, we can calculate the perimeter by adding the lengths of the sides:
Perimeter = AB + BC + AC
= 5 + √41 + 4
= 9 + √41 units
Therefore, the perimeter of triangle ABC is 9 + √41 units.