- Use 2 for the scalefactor.
- Find the imageof the otherpoint.
Repeat,but use a differentvaluefor the scalefactor.Whatseemsto be true aboutthe two images?Exploration 2- Drawa triangle.
- Selecta pointas the centerof dilation.Use one vertexof the triangle,or drawanotherpointfor the
center. - Use 2 for the scalefactor.
- Find the imageof the triangle.
- Repeat,but use a differentvaluefor the scalefactor.
Whatseemsto be true aboutthe two images?You can experimentfurtherwith differentfigures,centers,and scalefactors.Can you reachany conclusionsaboutimageswhenthe scalefactoris negative?You may havenoticedthat if point is dilated,the centeris , and the scalefactoris , , then
the imageof is on the sameside of as is. If the scalefactoris then the imageof is on
the oppositeside of. You may havealso also noticedthat a dilationwith a negativescalefactoris
equivalentto a dilationwith a positivescalefactorfollowedby a “reflectionin a point,”wherethe pointis the
centerof dilation.
This lessonbringsour studyof similarfiguresalmostto a close.We’ll revisitsimilarfiguresoncemorein
Chapter10, wherewe analyzethe perimeterand area of similarpolygons.Somewritershaveusedsimilarity
conceptsto explainwhy livingthingsare the “rightsize”and why, for example,thereare no -foot-tall
humangiants!
LessonExercises
Use the diagrambelowfor exercises1 - 10.
andA dilationhas the indicatedcenterand scalefactor. Completethe table.