On the basis of the meaning and general process of geometric proof through transformation concept and understanding the geometric properties of linear transformation, this study showed that the centroid of geometrical figure and certain properties of a parabola and an ellipse in school mathematics can be explained as a conservative properties through linear transformation. From an educational perspective, this is a good example of showing the process of how several existing individual knowledge can be reorganized by a mathematical concept. Considering the fact that mathematical usefulness of linear transformation can be revealed through an invariable and conservation concept, further discussion is necessary on whether the linear transformation map included in the former curriculum have missed its point.