Understanding the Problem
* Points: You have two points: (8, 3, 4) and (6, 1, 0).
* Distance Formula: We'll use the 3D distance formula, which is a generalization of the Pythagorean theorem:
Distance = √[(x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²]
Calculation
1. Label your points:
* (x₁, y₁, z₁) = (8, 3, 4)
* (x₂, y₂, z₂) = (6, 1, 0)
2. Plug the values into the distance formula:
Distance = √[(6 - 8)² + (1 - 3)² + (0 - 4)²]
3. Simplify:
Distance = √[(-2)² + (-2)² + (-4)²]
Distance = √(4 + 4 + 16)
Distance = √24
4. Find the square root (approximate):
Distance ≈ 4.899
Answer: The distance between the points (8, 3, 4) and (6, 1, 0) is approximately 4.899 units.