Two-dimensional points are represented as perpendicular distances from orthogonal axes, typically denoted as X and Y. For instance, (2,3) signifies a point 2 units from the y-axis and 3 units from the x-axis. If the coordinate axes are non-orthogonal, the point represents distances taken parallel to the axes.

[Image Source: Wikipedia]

In three dimensions, points are represented as distances from each of the three planes formed by the axes. For example, (2,3,4) represents a point 2 units from the YZ-plane, 3 units from the XZ-plane, and 4 units from the XY-plane.

Coordinates can be 'homogenized' by adding an extra value to the tuple. In three dimensions, points are represented as (x, y, z, w), which is equivalent to (x/w, y/w, z/w) in ordinary coordinates. This representation is commonly used in computer graphics as it facilitates expressing common operations, such as translation, as a linear map.