CK12 - Geometry

Note:The distancefrom the originto is WhenP rotates its imageis on the -axis,the samedistancefrom the originas. LessonSummary To ...

A line in the coordinateplanehas the equation Wheredoesthe line intersectthe -axis? Whatis the slopeof the line? The line is r ...

6. 7. 8. 9. 10. 11. 12. 13. wouldnot move.The productis equivalentto two rotations,whichis equivalentto a ro- tation,whichis eq ...

The shapebelowis movedwith a glide reflection.It is reflectedin the -axis,and the imageis then translated unitsto the right. In ...

A rotationis the sameas a rotationfollowedby a rotation.If is the matrixfor a polygon, then is the matrixfor the imageof in a ro ...

The imageof the originaltriangleis shownas the dashedtrianglebelow. The verticesare and. Vertices of left hand triangle are and ...

One pointon the originalstar, , is trackedas it is movedby the two reflections. Notethat: Star is right side up,Staris upsidedow ...

One pointon the originalarrowbox, , is trackedas it is movedby the two reflections. Notethat: Trapezoidis rotated to produceTrap ...

Doesgeometryhavea placein art and design?Mostpeoplewouldguessthat they do. We’ll get a chance to start to see how whenwe examine ...

Yes. Bothfinal imageswill be equivalentto translations,but the final imagescan be differentdistances from the originalpoint. ...

(Source:http://commons.wikimedia.org/wiki/File:Tile1.jpg,License:CreativeCommonsAttribution3.0 Un- ported) (Source:http://common ...

Whatis the sum of the measuresof the angles? is the sum of the anglemeasuresin any quadrilateral. Describewhichanglescometogethe ...

Apparentlysomeregularpolygonswill tessellateand somewon’t.You can explorethis morein the Lesson Exercises. Tessellatingwith Two ...

Notethat the samebasic“unit”can be usedto makedifferenttessellations. FurtherReading M. C. Escherwas a famoustwentieth-centurygr ...

Yes Yes Yes Yes Yes Equilateraltriangle,square,regularhexagon One exampleis shownhere Theseare regularhexagonswith equilateral ...

pointsymmetry planesof symmetry A planeof symmetrymay be a new concept,as it appliesto three-dimensionalobjects. Line Symmetry ...

In biologyline symmetryis calledbilateralsymmetry. The planerepresentationof a leaf, for example,may havebilateralsymmetry—itcan ...

In biologyrotationalsymmetryis calledradialsymmetry. The planerepresentationof a starfish,for example, may haveradialsymmetry—it ...

License) PointSymmetry We needto definesometermsbeforepointsymmetrycan be defined. Reflectionin a point:Points and are reflectio ...

If a figurehas pointsymmetryit has rotationalsymmetry. The converseis not true. If a figurehas rotationalsymmetryit may, or may ...