Google Classroom
GeoGebraGeoGebra Classroom

Fixed point of the plane isometry

Fixed points coincide with their image X=X'. Any direct isometry could be viewed as composition of rotation about origin and translation. The 3rd column of matrix representation A is image of origin, not center of rotation. Center is fixed point of isometry.
Experiment with arbitrary point X and its image X'. Could you write the equation for fixed points of the mapping?

Fixed points

It is easy to derive equation for fixed points: Gauss elimination (GeoGebra command ReducedRowEchelonForm) of the matrix (A-E) returns the equivalent echelon form Using back-substitution, unknown coordinates x, y can be solved for. Transformation has only one fixed point FP = (2.5, 3.5).