Introduction to Three Dimensional Geometry

Coordinate Axes and Octants

Three mutually perpendicular lines in space called the x, y, and z-axes divide the space into eight parts known as octants.

Coordinates of a Point in Space

Any point P in space is represented by an ordered triplet (x, y, z) representing its perpendicular distances from the yz, xz, and xy planes respectively.

Distance Formula

The straight-line distance between any two points P(x1, y1, z1) and Q(x2, y2, z2) in 3D space is calculated using an extension of the Pythagorean theorem.

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 concurrency of the medians of a triangle, whose 3D coordinates are simply the average of the x, y, and z coordinates of its three vertices.