A composition of transformations used to describe a congruence transformation is not unique. For example, the composition r(90,O) T maps the point (x,y) to (-y-2,x+5), as does the composition T r(90,O). Write another example of transformation composed of a translation composed of a translation followed by a 90 degree rotation, and then write an equivalent transformation composed of a 90 degree rotation followed by a translation. Show that each point (x,y) maps to the same point under both transformations.

Question

A composition of transformations used to describe a congruence transformation is not unique. For example, the composition r(90,O) T<5,2> maps the point (x,y) to (-y-2,x+5), as does the composition T<-2,5> r(90,O). Write another example of transformation composed of a translation composed of a translation followed by a 90 degree rotation, and then write an equivalent transformation composed of a 90 degree rotation followed by a translation. Show that each point (x,y) maps to the same point under both transformations.