Space coordinates

Read spatial coordinates and express distance and sphere conditions.

Meaning

Space coordinates use three perpendicular axes. Distance is the square root of the sum of squared coordinate differences; a sphere consists of points at fixed distance from a center.

Example

The distance from the origin to is so it lies on a sphere centered at the origin with radius 7.First, the squared distance in the horizontal plane is 2²+3². Use that distance and the perpendicular height 6 as the legs of another right triangle to obtain the spatial squared distance 2²+3²+6².A point in space needs three coordinates. Lengths in a paper projection are not automatically actual spatial distances.

Practice for this concept

Scope and references

Topics

Point positions in space, distances, sphere equations

Learning goal

Read spatial coordinates and express distance and sphere conditions.

Helpful background

Extend plane coordinates to three spatial directions.