Multiplicationof a polygonmatrixby one of the specialmatrices , , or will reflect
the polygonin the -axis,the -axis,or the line respectively.
Pointsto Consider
You saw in this lessonthat reflectionscorrespondto multiplicationby a particularmatrix.You mightbe inter-
estedto investigatehow multiplicationon the right of a polygonmatrixby one of the followingmatrices
changesthe originalmatrix.
As if matrixarithmeticis not “different”enough,in an upcominglessonwe’ll see that thereis anotherkind
of multiplicationcalledscalarmultiplication.Scalarmultiplicationwill enableus to use matricesto represent
dilationsin the coordinateplane.
LessonExercises
- Provethat reflectionin the line is an isometry.
Given: and , its reflectionin
Prove:
Let , and.
Write the matrixfor eachproduct.