Homogeneous coordinates are a mathematical representation used in projective geometry to simplify the handling of points in space. In this system, a point in two-dimensional space is represented by three coordinates (x, y, w), where w is a non-zero scaling factor. This allows for the representation of points at infinity, which is useful in computer graphics and geometric transformations. In homogeneous coordinates, the actual Cartesian coordinates can be obtained by dividing the first two coordinates by w. For example, the point (x, y, w) corresponds to the Cartesian point (x/w, y/w). This approach facilitates operations like translation, rotation, and scaling in a unified manner, making it essential in fields such as computer graphics and robotics.