10.1 The 3D Coordinate System
Distance and Midpoint Formulas
d = √(x₂-x₁)² + (y₂ - y₁)² + (z₂-z₁)²
((x₁ + x₂)/2, (y₁+ y₂)/2, (z₁ +z₂)/2)
d = √(x₂-x₁)² + (y₂ - y₁)² + (z₂-z₁)²
((x₁ + x₂)/2, (y₁+ y₂)/2, (z₁ +z₂)/2)
The Equation of a Sphere
A sphere with center (h,j,k) and radius r is defined as the set of all points (x,y,z) such that the distance between (x, y,z).
(z - h)² + (y - k)² + (z - j)² = r²
A sphere with center (h,j,k) and radius r is defined as the set of all points (x,y,z) such that the distance between (x, y,z).
(z - h)² + (y - k)² + (z - j)² = r²