CK12 - Geometry

Sincethe endpointsof and movedthe samedistancehorizontallyand vertically, both segments
havethe samelength.

Translationis an Isometry

Anisometryis a transformationin whichdistanceis “preserved.”This meansthat the distancebetween
any two pointsis the sameas the distancebetweenthe imagesof the points.

Did you noticethis in example1 above?

(sincethey are both equalto )

Would we get the sameresultfor any otherpointin this translation?Yes. It’s clearthat for any point ,

the distancefrom to will be. Everypointmoves unitsto its image.

This is true in general.

TranslationIsometryTheoremEverytranslationin the coordinateplaneis an isometry.

You will provethis theoremin the LessonExercises.

Vectors

Let’s look at the translationin example1 in a slightlydifferentway.

Example 2

The point in a translationis the point. Whatis the imageof in the same
translation?

The arrowfrom to is calledavector, becauseit has alengthand adirection. The horizontaland

verticalcomponentsof the vectorare and respectively.