How does the 3D coordinate system work?

• In three-dimensional space we can label where any object is using the?x-y-z?coordinate system
• In the 3D cartesian system, the?x-?and?y-?axes usually represent lateral space (length and width) and the?z-axis represents vertical height

What can we do with 3D coordinates?

• If we have two points with coordinates (x₁?, y₁?, z₁)?and?(x₂?, y₂?, z₂)?then we should be able to find:
  • The?midpoint?of the two points
  • The?distance?between the two points
• If the coordinates are labelled A and B then the line segment between them is written with the notation [AB]

How do I find the midpoint of two points in 3D?

• The midpoint is the?average (middle) point
  • It can be found by finding the middle of the?x-coordinates and the middle of the?y-coordinates
• The coordinates of the midpoint will be

• • This is given in the formula booklet, you do not need to remember it

How do I find the distance between two points in 3D?

• The distance between two points with coordinates ((x₁?, y₁?, z₁)?and?(x₂?, y₂?, z₂)?can be found using the formula

• • This is given in the formula booklet, you do not need to remember it