Introduction to Three Dimensional Geometry

Coordinate Axes and Planes in 3D

Space is determined by three mutually perpendicular lines called the X, Y, and Z axes, which divide the space into eight parts known as octants.

Coordinates of a Point in Space

Any point P in three-dimensional space is represented by an ordered triplet (x, y, z), representing its perpendicular distances from the three coordinate planes.

Distance Formula

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

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