10 Which one of these cards has a Rotational Order of Symmetry = 2?
11 Note 1: Total order of symmetry (Line Symmetry)Total order of SymmetryNumber of Axes of SymmetryOrder of Rotational Symmetry=+
12 ShapeAxes of SymmetryOrder of Rotational SymmetryTotal Order of Symmetry484221126612
13 Task !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 ?
14 Note 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
16 Note 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.
17 Reflection 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
18 Analyze 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
19 To 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.
24 What 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
25 Drawing Rotations ¼ turn clockwise = 90º clockwise BCRotate about point A¼ turn clockwise =90º clockwiseAB’DD’C’
26 To 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.
27 Examples 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
28 RotationIn 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
29 180º By what angle is this flag rotated about point C ? Remember: Rotation is always measured in the anti clockwise direction!
30 By what angle is this flag rotated about point C ? 90º
31 By what angle is this flag rotated about point C ? 270º
32 Define 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
33 Translations 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’
35 Translate the shape ABCDEF by the vector to give the image A`B`C`D`E`F`. ( )- 4- 2
36 EnlargementIn enlargement, all lengths and distances from a point called the centre of enlargement are multiplied by a scale factor (k).
37 To 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.
38 Enlarge the ABC by a scale factor of 2 using the point O as the centre of enlargement.
39 To 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.
40 Calculating the scale factor To calculate the scale factor (k) we use the formula :Scale factor (k) ==
41 Negative 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.
43 Do 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
44 Reflect 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
45 Do Now: What transformations are in each example? 1.2.3.RotationEnlargementReflection4.5.TranslationReflection
46 Do 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
47 Koru DesignUsing the templates provided, or your own, create a pattern of at least 5 transformations, which consists of at least:One reflectionOne translationOne rotation
48 How 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
49 Now its your turn!Write the appropriate instruction for each transformation, in the order that it appears.A’’’A’’’’A’’P6 cm5 cmAA’M
50 Writing 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
51 Writing 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
52 Koru 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.
54 or 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
55 Exchange your Work Logo Creators Backyard Designers Follow your partners instructions and recreate their logoBackyard DesignersMark your partners work against the marking sheet