Introduction to Three Dimensional Geometry

Coordinate Axes and Planes in 3D

Three mutually perpendicular lines called the X-axis, Y-axis, and Z-axis intersect at the origin (0,0,0) and divide the space into three coordinate planes: XY, YZ, and ZX planes.

Octants

Unlike the 4 quadrants in 2D geometry, the three coordinate planes divide 3D space into 8 regions known as octants, designated as I to VIII based on the signs of the coordinates (x, y, z).

Distance Formula in 3D

The straight-line distance between any two points P(x1, y1, z1) and Q(x2, y2, z2) in space is given by the square root of the sum of squared differences of their corresponding coordinates.

Section Formula

Used to find the coordinates of a point that divides the line segment joining two given points in a specific ratio, both internally and externally.

Centroid of a Triangle

The point of concurrence of the medians of a triangle, whose 3D coordinates are found by taking the arithmetic mean of the x, y, and z coordinates of its three vertices.