This study analyses the students' performances in two-dimensional transformation geometry and explores the mistakes made by the students taking the analytic geometry course given by researchers. An examination was given to students of Education Faculties who have taken the analytic geometry course at Eskisehir Osmangazi University in Turkey. The subject of this study included 126 third-year students in the Department of Mathematics Education. Data were collected from a seven questions exam. This exam consisted of three procedural questions, two conceptual questions and two procedural-conceptual questions. In data analysis, a descriptor code key was used. When the students' overall performances were considered for all seven questions, the results showed that they did not understand how to apply rotation transformation. The mostly observed mistakes showed that the students seemed to know the algebraic meaning of translation and also rotation but they did not seem to understand the geometric meaning of them. (Contains 4 tables.)