Algebra - Geometry and measurement in two and three dimensions — The 3D orthogonal coordinate system

About this lesson

This unit introduces the three-dimensional orthogonal coordinate system in space. It explains how to determine the position of a point using three mutually perpendicular axes, following the right-hand rule, and defines the Cartesian planes (xy, xz, yz) by their equations (z=0, y=0, x=0). Students learn to plot points given their coordinates (x, y, z) by first locating the projection in the xy-plane and then moving along the z-axis. The unit also covers calculating the distance between two points in space using the distance formula, proving geometric properties like right-angled or equilateral triangles, and finding the coordinates of the midpoint of a line segment joining two points. Worked examples and exercises involve identifying points, computing distances, verifying triangle types, and solving for unknown coordinates or midpoints, often using cuboids or cubes as visual aids.