Fixed point of the plane isometry

Fixed points coincide with their image X=X'.[br]Any direct isometry could be viewed as composition of rotation about origin and translation. The 3[sup]rd[/sup] 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:[br][img]data:image/png;base64,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[/img][br]Gauss elimination (GeoGebra command [code]ReducedRowEchelonForm[/code]) of the matrix (A-E) returns the equivalent echelon form[br][img]data:image/png;base64,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[/img][br] Using back-substitution, unknown coordinates x, y can be solved for. [br][br][img]data:image/png;base64,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[/img][br][br]Transformation has only one fixed point FP = (2.5, 3.5). [br][br]

Information: Fixed point of the plane isometry