homogeneous coordinates

Homogeneous coordinates mean these coordinates are extended with any k multiplier value which is not zero. For instance, in 2D, we have a point, (x, y). If this point is extended a k multiplier both values and dimension, it changes as (kx, ky, k). In addition changed point can be divided by k value, it equals (kx / k, ky / k, k / k) or (x, y, 1) and this triple coordinate point is homogeneous coordinate point. If k is 0, x and y values become infinite and this homogeneous coordinate point refer to infinite point in 2D coordinate system. When the point has 3 real values like (x, y, z), as in 2D it is also extended any k multiplier value and if the k value is 0, this point refer to infinite plane in 3D coordinate system.