IB DP Maths: AI SL复习笔记3.2.1 3D Coordinate Geometry

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