Answer: To find the length of the horizontal sides of the rhombus, we need to find the distance between points (1, 3) and (9, 7), which is the same as the distance between points (4, 7) and (6, 3).
Using the distance formula:
d = √[(x₂ - x₁)² + (y₂ - y₁)²]
d = √[(9 - 1)² + (7 - 3)²]
d = √[64 + 16]
d = √80
d ≈ 8.94
So the length of the horizontal sides of the rhombus is approximately 8.94 units.
To find the perimeter of the rhombus, we need to find the distance between all four vertices and add them up.
Using the distance formula:
d₁ = √[(4 - 1)² + (7 - 3)²] = √25 = 5
d₂ = √[(9 - 4)² + (7 - 7)²] = √25 = 5
d₃ = √[(6 - 9)² + (3 - 7)²] = √16 + 16 = √32 ≈ 5.66
d₄ = √[(1 - 6)² + (3 - 7)²] = √25 + 16 = √41 ≈ 6.40
Perimeter = d₁ + d₂ + d₃ + d₄ = 5 + 5 + 5.66 + 6.40 ≈ 22.06
So the perimeter of the rhombus is approximately 22.06 units.
Explanation: