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This lessonwas abouttwo-dimensionalspacerepresentedby a coordinategrid. But we knowthereare
morethan two dimensions.The real worldis actuallymultidimensional.Vectorsare well suitedto describe
motionin that world.Whatwouldtransformationvectorslook like there?
LessonExercises
- Provethat any translationin the coordinateplaneis an isometry. Given:A translationmovesany point
unitshorizontallyand unitsvertically.Let and be pointsin the coordinateplane.
Prove:
[Hint:Express and in termsof and .]
- A trianglehas vertices , and. The vectorfor a translationis
. [Example3] How doesthis transformationmovethe originaltriangle? - Write a transformationvectorthat wouldmovethe solid figureto the red figure.
- The transformationvector movesa pointto the point. Whatare the coordinates
of the originalpoint? - Write a transformationvectorthat wouldmovethe point to the origin.
- How doesthe translationvector movea figure?
- The point is movedby the translationvector. How far doesthe originalpointmove?
- Write a translationvectorthat will moveall points units.