Answer:
Perimeter = 4(√2 + √5) units
Explanation:
Given:
Quadrant of 4 points;
A(3, 5) B(1, 3) C(3, -1) D(5, 3)
Find:
Perimeter
Computation:
Distance = √(x1 - x2)² + (y1 - y2)²
Distance between AB = √(3 - 1)² + (5 - 3)²
Distance between AB = √4 + 4
Distance between AB = 2√2 units
Distance between BC = √(1 - 3)² + (3 + 1)²
Distance between BC = √4 + 16
Distance between BC = 2√5 units
Distance between CD = √(3 - 5)² + (-1 - 3)²
Distance between CD = √4 + 16
Distance between CD = 2√5 units
Distance between DA = √(5 - 3)² + (3 - 5)²
Distance between DA = √4 + 4
Distance between DA = 2√2 units
Perimeter = sum of all sides
Perimeter = 2√2 + 2√5 + 2√2 + 2√5
Perimeter = 4√2 + 4√5
Perimeter = 4(√2 + √5) units