One pointon the originalarrowbox, , is trackedas it is movedby the two reflections.
Notethat:
Trapezoidis rotated to produceTrapezoid'.is unitsabovethe -axis. is unitsbelowthe -axis.LessonSummary
A compositionis a combinationof two (or more)transformationsthat are appliedin a specificorder. You
saw examplesof severalkindsof compositions.
- Glidereflection
- Two rotations
- Reflectionin parallellines
- Reflectionin intersectinglines
Thesecompositionsare combinationsof transformationsthat are isometries.The compositionsare themselves
isometries.
For someof the compositionsin this lessonyou saw a matrixoperationthat can be usedto find the image
of a pointor polygon.Also,you saw that in somecasesthereis a simplebasictransformationthat is
equivalentto a composition.
Pointsto Consider
In this lessonyou studiedcompositionsof isometries,whichare also isometries.We knowthat thereare
othertransformationsthat are not isometries.The primeexampleis the dilation.We returnto dilationsin a
later lesson,wherea secondtype of multiplicationof a matrixis introduced.