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Translations, rotations, reflections, and dilations

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  • 1. Translations, Rotations,Reflections, and Dilations.

2. In geometry, atransformation is a wayto change the positionof a figure. 3. In some transformations, the figureretains its size and only its position ischanged.Examples of this type of transformationare:translations, rotations, and reflectionsIn other transformations, such asdilations, the size of the figure willchange. 4. TRANSLATION 5. TRANSLATIONA translation is a transformation thatslides a figure across a plane or throughspace.With translation all points of a figuremove the same distance and the samedirection. 6. TRANSLATIONBasically, translation means that a figurehas moved.An easy way to remember whattranslation means is to rememberA TRANSLATION IS A CHANGE IN LOCATION.A translation is usually specified by adirection and a distance. 7. TRANSLATIONWhat does a translation look like?original imagex yTranslate from x to yA TRANSLATION IS A CHANGE IN LOCATION. 8. TRANSLATIONIn the example below triangle A is translated tobecome triangle B.A BDescribe the translation.Triangle A is slide directly to the right. 9. TRANSLATIONIn the example below arrow A is translated tobecome arrow B.ABDescribe the translation.Arrow A is slide down and to the right. 10. ROTATION 11. ROTATIONA rotation is a transformation that turns afigure about (around) a point or a line.Basically, rotation means to spin a shape.The point a figure turns around is calledthe center of rotation.The center of rotation can be on oroutside the shape. 12. ROTATIONWhat does a rotation look like?center of rotationA ROTATION MEANS TO TURN A FIGURE 13. ROTATIONThe trianglewas rotatedaround theThis is another way rotation lookspoint.center of rotationA ROTATION MEANS TO TURN A FIGURE 14. ROTATIONIf a shape spins360, how far doesit spin?360This is called . 15. ROTATIONIf a shape spins180, how far doesit spin?Rotating a shape 180 turnsa shape upside down.This is called a . 180 16. ROTATIONIf a shape spins 90,how far does itspin?This is called a .90 17. ROTATIONDescribe how the triangle A was transformed tomake triangle BA BDescribe the translation.Triangle A was rotated right 90 18. ROTATIONDescribe how the arrow A was transformed to makearrow BABDescribe the translation.Arrow A was rotated right 180 19. ROTATIONWhen some shapes are rotated theycreate a special situation calledrotational symmetry.to spin a shape the exact same 20. ROTATIONAL SYMMETRYA shape has rotational symmetry if, afteryou rotate less than one full turn, it is thesame as the original shape.Here is an exampleAs this shape is rotated 360, is itever the same before the shapereturns to its original direction?Yes, when it is rotated 90 it is thesame as it was in the beginning.So this shape is said to haverotational symmetry.90 21. ROTATIONAL SYMMETRYA shape has rotational symmetry if, afteryou rotate less than one full turn, it is thesame as the original shape.Here is another exampleAs this shape is rotated 360, is itever the same before the shapereturns to its original direction?Yes, when it is rotated 180 it is thesame as it was in the beginning.So this shape is said to have180 rotational symmetry. 22. ROTATIONAL SYMMETRYA shape has rotational symmetry if, afteryou rotate less than one full turn, it is thesame as the original shape.Here is another exampleAs this shape is rotated 360, is itever the same before the shapereturns to its original direction?No, when it is rotated 360 it isnever the same.So this shape does NOT haverotational symmetry. 23. ROTATION SYMMETRYDoes this shape have rotational symmetry?120Yes, when theshape is rotated120 it is thesame. Since 120 is less than 360,this shape HASrotationalsymmetry 24. RREEFFLLEECCTTIIOONN 25. REFLECTIONA reflection is a transformation that flipsa figure across a line.A REFLECTION IS FLIPPED OVER A LINE. 26. REFLECTIONRemember, it is the same, but itAfter a shape is is reflected, backwardsit looks like amirror image of itself.A REFLECTION IS FLIPPED OVER A LINE. 27. REFLECTIONNotice, The line the that shapes a shape are is exactly flipped the over sameisdistance called a line from of the reflection.line of reflection onboth sides.of reflection can be on the shapeor it can be outside the shape.Line of reflectionA REFLECTION IS FLIPPED OVER A LINE. 28. REFLECTIONDetermine if each set of figures shows a reflection or atranslation.AC BC BAA REFLECTION IS FLIPPED OVER A LINE. 29. REFLECTIONSometimes, a figure hasreflectional symmetry.This means that it can be folded along a line ofreflection within itself so that the two halves of thefigure match exactly, point by point.Basically, if you can fold a shape in half and itmatches up exactly, it has reflectional symmetry. 30. REFLECTIONAL SYMMETRYAn easy way to understand reflectional symmetry is tothink about folding.Do you rememberfolding a piece ofpaper, drawing halfof a heart, and thenWhat happens whenyou unfold the pieceof paper?cutting it out? 31. REFLECTIONAL SYMMETRYReflectionalSymmetryThe line of reflectionmeans The two that halves a shapearein a figure withcan The exactly be two folded halves the samealong makeareflectionalline a whole of They reflection areheart.sosymmetry is called athe symmetrical.two haves of theline of symmetry.figure match exactly,point by point.Line of Symmetry 32. REFLECTIONAL SYMMETRYThe line created by the fold is the line of symmetry.A shape can have more than one line of symmetry.How can I foldthis shape sothat it matchesWhere is the line of symmetry for this shape?exactly?Line of Symmetry 33. REFLECTIONAL SYMMETRYHow many lines of symmetry does each shape have?Do you see a pattern? 34. REFLECTIONAL SYMMETRYWhich of these flags have reflectional symmetry?United States of AmericaMexicoCanadaEngland 35. CONCLUSIONWe just discussed three types of transformations.See if you can match the action with theappropriate transformation.FLIPSLIDETURNREFLECTIONTRANSLATIONROTATION 36. Translation, Rotation, and Reflection allchange the position of a shape, while thesize remains the same.The fourth transformation that we aregoing to discuss is called dilation. 37. DILATIONDilation changes the size of the shapewithout changing the shape.When you go to the eye doctor, theydilate you eyes. Lets try it by turning offthe lights.When you enlarge a photograph or use acopy machine to reduce a map, you aremaking dilations. 38. DILATIONEnlarge means to make a shape bigger.Reduce means to make a shape smaller.The scale factor tells you how muchsomething is enlarged or reduced. 39. DILATIONNotice each time the shape transforms the shapestays the same and only the size changes.25000%%ERNELDAURCGEE 40. DILATIONLook at the pictures belowDilate the image with a scale factorof 75%Dilate the image with a scale factorof 150% 41. DILATIONLook at the pictures belowDilate the image with a scale factorof 100%Why is a dilation of 75% smaller, adilation of 150% bigger, and a dilation of100% the same? 42. Lets try to make sense of all of thisTRANSFORMATIONSCHANGE THE POSTIONOF A SHAPECHANGE THE SIZE OF ASHAPETRANSLATION ROTATION REFLECTIONChange inlocationTurn around apointFlip over alineDILATIONChange size ofa shape 43. See if you can identify the transformation thatcreated the new shapesTRANSLATION 44. See if you can identify the transformation thatcreated the new shapesWhere is the line REFLECTIONof reflection? 45. See if you can identify the transformation thatcreated the new shapesDILATION 46. See if you can identify the transformation thatcreated the new shapesROTATION 47. See if you can identify the transformation in thesepictures?REFLECTION 48. See if you can identify the transformation in thesepictures?ROTATION 49. See if you can identify the transformation in thesepictures?TRANSLATION 50. See if you can identify the transformation in thesepictures?DILATION 51. See if you can identify the transformation in thesepictures?REFLECTION

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