Homogeneous coordinates are a mathematical representation used in projective geometry to simplify the handling of geometric transformations. 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 easier manipulation of points, especially when dealing with transformations like translation, rotation, and scaling. One key advantage of homogeneous coordinates is that they enable the representation of points at infinity, which is useful in computer graphics and robotics. By using homogeneous coordinates, operations such as perspective projection can be performed more efficiently, making them essential in fields like computer vision and 3D modeling.