MathDB
composition of center and axis symmetry

Source: Spanish Mathematical Olympiad 1981 P6

December 23, 2022
geometric transformationvectorsymmetrylinear algebra

Problem Statement

Prove that the transformation product of the symmetry of center (0,0)(0, 0) with the symmetry of the axis, with the line of equation x=y+1x = y + 1, can be expressed as a product of an axis symmetry the line ee by a translation of vector v\overrightarrow{v}, with ee parallel to v\overrightarrow{v}, . Determine a line ee and a vector v\overrightarrow{v}, that meet the indicated conditions. have to be unique ee and v\overrightarrow{v},?