How to Calculate Distance in 3D Space

The Organic Chemistry Tutor

This educational video provides a comprehensive tutorial on calculating the distance between two points in three-dimensional space. The lesson begins by introducing the 3D distance formula and applying it to a specific problem with given coordinates. The narrator then transitions from simple calculation to geometric visualization, plotting the points on a 3D coordinate system (x, y, z axes) to show exactly where they sit in space. This visual approach helps students understand the spatial relationship between the points rather than just crunching numbers. The video explores key mathematical themes including 3D coordinate geometry, the application of the Pythagorean Theorem in multiple dimensions, and algebraic derivation. A significant portion of the video is dedicated to deriving the distance formula from scratch. By constructing right triangles within a 3D rectangular prism, the narrator demonstrates how the 3D formula is essentially the Pythagorean Theorem applied twice—first to find the diagonal of the base, and second to find the diagonal through space. For educators, this video is an excellent resource for bridging the gap between 2D and 3D geometry. It addresses the common student struggle of visualizing three-dimensional problems on a two-dimensional surface. The step-by-step derivation is particularly valuable for higher-level math classes, as it moves beyond rote memorization to foster a deep conceptual understanding of *why* the formula works. Teachers can use this video to introduce 3D vectors, prepare for calculus concepts, or reinforce algebra skills through geometric proofs.