Abstract: This paper is focused on geometric representation of graphics transformations, and makes an improvement on the methods of transformation description, commonly given in text books with the homogenous coordinate matrix in separation. Based on affine transform theory and geometry computing theory and algorithm, geometric representation of graphics transformation is probed in the paper. By associating graphics transformation with basic geometry, various fundamental transformations, including translation, rotation, shear, symmetry and scale, are unified through a homogenous matrix constructed by a solution in terms of directed lines.