5.
6.
7.
8.
- Placethe originalsegmentso that one endpointis on the top horizontalline. Slantthe segmentso that
the otherendpointis on the seventhhorizontalline belowthe top line. Theseeighthorizontallinesdivide
the originalsegmentinto sevencongruentsmallersegments.
SimilarityTransformations
LearningObjectives
- Drawa dilationof a givenfigure.
- Plot the imageof a pointwhengiventhe centerof dilationand scalefactor.
- Recognizethe significanceof the scalefactorof a dilation.
Introduction
Earlieryou studiedone groupof transformationsthat “preserve”length.This meansthat the imageof a
segmentis a congruentsegment.Thesecongruencetransformationsare translations,reflections,and
rotations.
In this lesson,you’llstudyone morekind of transformation,thedilation. Dilationsdo not preservelength,
meaningthe imageof a segmentcan be a segmentthat is not congruentto the original.You’ll see that the
imageof a figurein a dilationis a similar, not necessarilycongruent,figure.
Dilations
A dilationis like a “blow-up”of a phototo changeits size.A dilationmay makea figurelarger, or smaller,
but the sameshapeas the original.In otherwords,as you’llsee, a dilationgivesus a figuresimilarto the
original.
Adilationis a transformationthat has acenterand ascalefactor. The centeris a pointand the scale
factorgovernshow muchthe figurestretchesor shrinks.
Thinkaboutwatchinga roundballoonbeinginflated,and focusingon the pointexactlyin the middleof the
balloon.The balloonstretchesoutwardsfrom this pointuniformly. So for example,if a circleis drawnaround
the point,this circlewill growas the balloonstretchesawayfrom the points.
Dilationwith centerat point and scalefactor ,Givena point that is unitsfrom point. The imageof for this dilationis the point that is
collinearwith and and unitsfrom , the centerof dilation.Example 1