12. Transformations...........................................................................................................................
Translations
LearningObjectives
- Grapha translationin a coordinateplane.
- Recognizethat a translationis an isometry.
- Use vectorsto representa translation.
Introduction
Translationsare familiarto you from earlierlessons.In this lesson,we restateour earlierlearningin terms
of motionsin a coordinateplane.We’ll use coordinatesand vectorsto expressthe resultsof translations.
Translations
Rememberthat a translationmoveseverypointa givenhorizontaldistanceand/ora givenverticaldistance.
For example,if a translationmovesthe point unitsto the right and unitsup, to then
this translationmoveseverypointthe sameway.
The originalpoint(or figure)is calledthepreimage, in this case. The translatedpoint(or figure)
is calledtheimage, in this case , and is designatedwith the primesymbol.
Example 1
The point in a translationbecomesthe point. Whatis the imageof in the
sametranslation?
Point moved unit to the left and unitsdownto reach. will also move unit to the left and
unitsdown.is the imageof.Noticethe following: