10Which one of these cards has a Rotational Order of Symmetry = 2?
11Note 1: Total order of symmetry (Line Symmetry)Total order of SymmetryNumber of Axes of SymmetryOrder of Rotational Symmetry=+
12ShapeAxes of SymmetryOrder of Rotational SymmetryTotal Order of Symmetry484221126612
13Task !Choose 3 objects in the room and describe their axes of symmetry, order of rotational symmetry and total order of symmetry.Can you find an object with a total order of symmetry greater than 4 ?
14Note 1: Total order of symmetry Total order of symmetry = the number of axes of symmetry + order of rotational symmetry. The number of axes of symmetry is the number of mirror lines that can be drawn on an object.The order of rotational symmetry is how many times the object can be rotated to ‘map’ itself. (through an angle of 360° or less)IWB Ex pgEx pg 750
16Note 2: ReflectionA point and its image are always the same distance from the mirror lineIf a point is on the mirror line, it stays there in the reflection. This is called an invariant point.
17Reflection To draw an image: Measure the perpendicular distance from each point to the mirror line.Measure the same perpendicular distance in the opposite direction from the mirror line to find the image point. (often it is easier to count squares). e.g. Draw the image of PQR in the mirror line LM.IWB Ex 26.01pg
18Analyze the ALPHABET ALPHABET Notice the letter B, H and E are unchanged if we take their horizontal mirror image? Can you think of any other letters in the alphabet that are unchanged in their reflection?What is the longest word you can spell that is unchanged when placed on a mirror?Can you draw an accurate reflection of your own name?IWB Ex 26.02pg
19To draw a mirror line between a point and it’s reflection: 1. Construct the perpendicular bisector between the point and it’s image.e.g. Find the mirror line by which B` has been reflected from B.
24What are these equivalent angles of Rotation? Rotations are always specified in the anti clockwise directionWhat are these equivalent angles of Rotation?270° Anti clockwise is _______ clockwise180 ° Anti clockwise is ______ clockwise340 ° Anti clockwise is _______ clockwise
25Drawing Rotations ¼ turn clockwise = 90º clockwise BCRotate about point A¼ turn clockwise =90º clockwiseAB’DD’C’
26To draw images of rotation: Measure the distance from the centre of rotation to a point.Place the protractor on the shape with the cross-hairs on the centre of rotation and the 0o towards the point.Mark the wanted angle, ensuring to mark it in the anti-clockwise direction.Measure the same distance from the centre of rotation in the new direction.Repeat for as many points as necessary.
27Examples Rotate flag FG, 180 about O Draw the image A`B`C`D` of rectangle ABCD if it is rotated 90o about point A.A
28RotationIn rotation every point rotates through a certain angle about a fixed point called the centre of rotation.Rotation is always done in an anti-clockwise direction.A point and it’s image are always the same distance from the centre of rotation.The centre of rotation is the only invariant point.Rotation game
29180º By what angle is this flag rotated about point C ? Remember: Rotation is always measured in the anti clockwise direction!
30By what angle is this flag rotated about point C ? 90º
31By what angle is this flag rotated about point C ? 270º
32Define these terms Mirror line Centre of rotation Invariant The line equidistant from an object and its imageThe point an object is rotated aboutDoesn’t changeMirror lineCentre of rotationInvariantWhat is invariant inReflectionrotationThe mirror lineThe size of angles and sidesThe area of the shapeCentre of rotationSize of angles and sides
33Translations Each point moves the same distance in the same direction There are no invariant points in a translation(every point moves)
34( ) ( ) Vectors Vectors describe movement x y ← movement in the x direction (left and right)y← movement in the y direction (up and down)Each vertex of shape EFGH moves along the vector( )-3-6To become the translated shape E’F’G’H’
35Translate the shape ABCDEF by the vector to give the image A`B`C`D`E`F`. ( )- 4- 2
36EnlargementIn enlargement, all lengths and distances from a point called the centre of enlargement are multiplied by a scale factor (k).
37To draw an enlargementMeasure the distance from the centre of enlargement to a point.Multiply the point by the scale factor and mark the point’s image point.Continue for as many points as necessary.
38Enlarge the ABC by a scale factor of 2 using the point O as the centre of enlargement.
39To find the centre of enlargement Join each of the points to it’s image point.The point where all lines intersect is the centre of enlargement.
40Calculating the scale factor To calculate the scale factor (k) we use the formula :Scale factor (k) ==
41Negative Scale Factors When the scale factor is negative, the image is on the opposite side of the centre of enlargement from the object.To draw images of negative scale factors:Measure the distance from the centre of rotation to a point.Multiply the distance by the scale factor.Measure the distance on the opposite side of the centre of rotation from the point.Repeat for as many points as necessary.
43Do Now: Match up the terms with the correct definition Write them into your vocab listCuts a line into two equal parts (cuts it in half) – also called the mediatorThe transformed objectA transformation which maps objects across a mirror lineA line which intersects a line at right anglesThe line in which an object is reflectedImageMirror linePerpendicularBisectorReflection
44Reflect the shape in the red mirror line, translate the image by the vector Enlarge the image scale factor 3, centre P Rotate 45o , centre A’’’AP
45Do Now: What transformations are in each example? 1.2.3.RotationEnlargementReflection4.5.TranslationReflection
46Do Now1.) Reflection is a transformation which maps an object across a __________.2.) In rotation, the only invariant point is called the __________________.3.) A _______ describes the movement up and down, and across, in a translation.4.) All of the _________ points in reflection lie on the mirror line.5.) The area of the object, the size of the angles and the length of the sides are invariant in both rotation and ___________mirror linecentre of rotationvectorinvariantreflectioninvariant, centre of rotation, reflection, vector, mirror line
47Koru DesignUsing the templates provided, or your own, create a pattern of at least 5 transformations, which consists of at least:One reflectionOne translationOne rotation
48How to Write Instructions Reflect ABCD through the mirror line (M)Translate the image A’B’C’D’ 4 cm to the rightRotate the image A’’B’’C’’D’’, 90o counter clockwise about the point P.4 cmMP
49Now its your turn!Write the appropriate instruction for each transformation, in the order that it appears.A’’’A’’’’A’’P6 cm5 cmAA’M
50Writing Instructions ( ) → ( ) 1.) Label your object 2.) Reflect image about mirror line M3.) Translate the imagea’b’c’d’ by the vector( ) → ( )4.) Rotate the image a’’b’’c’’d’’ about point P 90ºMbcc’b’x421y-7add’a’c’’b’’3b’’’a’’’d’’a’’4c’’’d’’’P
51Writing Instructions ( ) to give image a’’’b’’’c’’’ 1.) Construct equilateral triangle abc(Label your object)2.) Rotate object abc 90º about point P to give a’b’c’.3.) Reflect image a’b’c’ through mirror line M to give image a’’b’’c’’4.) Translate the object a’’b’’c’’ by the vector( ) to give image a’’’b’’’c’’’c’’’4b’’’ba’’’1acPc’c’’b’b’’23a’a’’8M4
52Koru DesignUsing the templates provided, or your own, create a pattern of at least 5 transformations, which consists of at least:One reflectionOne translationOne rotation* Write a set of instructions so another student could reproduce your pattern.
54or Choose a Task Design a Logo “The Backyard” (You have 20 minutes to complete it!)Design a LogoUsing at least 2 different construction techniques and at least 2 different types of transformations with Instructions“The Backyard”Follow the set of instructions to complete a plan of a backyard.or
55Exchange your Work Logo Creators Backyard Designers Follow your partners instructions and recreate their logoBackyard DesignersMark your partners work against the marking sheet