To find the perimeter of a triangle with vertices at (-5, 5), (3, 5), and (3, -2), we need to calculate the distances between each pair of vertices and then sum them up.
Let's denote the vertices as follows:
A (-5, 5)
B (3, 5)
C (3, -2)
The distance between two points (x₁, y₁) and (x₂, y₂) is given by the distance formula:
Distance = √((x₂ - x₁)² + (y₂ - y₁)²)
So, the distance between points A and B is:
AB = √((3 - (-5))² + (5 - 5)²)
= √((3 + 5)² + 0²)
= √(8²)
= √64
= 8
The distance between points B and C is:
BC = √((3 - 3)² + (-2 - 5)²)
= √(0² + (-7)²)
= √49
= 7
The distance between points C and A is the same as AB, since they share the same y-coordinate:
CA = AB = 8
Now, we sum up the distances to find the perimeter:
Perimeter = AB + BC + CA
= 8 + 7 + 8
= 23
So, the perimeter of the triangle is 23 units.
