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Symmetry 1. Line Symmetry - A shape has line symmetry if it can fold directly onto itself. - The line of folding (mirror line) is called an axis of symmetry e.g. Draw in the lines of symmetry for the following shapes 0 lines of symmetry An infinite number of lines of symmetry 2. Rotational Symmetry - the order of rotational symmetry is the number of times a figure maps exactly onto itself during a turn of 360° - Every shape has an order of rotational symmetry of at least one. e.g. State the order of rotation for the following shapes Order of 1 An infinite order of rotational symmetry Order of 4 4 lines of symmetry

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Point Symmetry - Occurs when an object maps onto itself after a half turn or a turn of 180° e.g. Which of the following shapes has point symmetry? YESNO 3. Total Order of Symmetry - Is the number of lines (axes) of symmetry plus the order of rotational symmetry. e.g. State the total order of symmetry for the following shapes Order of 1Order is ∞ Total Order of Symmetry = 8 Total Order of Symmetry = 1 Total Order of Symmetry is infinite Order of 4 4 lines of symmetry 0 lines of symmetry ∞ lines of symmetry

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Reflection e.g. Reflect the following objects in mirror line m. m Properties: - Reflected lines, angles and areas remain the same size - Points on the mirror line are invariant - Sense or orientation is reversed - In reflection, an object and its image are on the opposite sides of the mirror line - The object and its image are ALWAYS the same distance from the mirror line A B C A’ B’ m C’ Note: We use a dash after the letters to show which is the image AA’ CC’ BB’

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e.g. Draw in the mirror line for the following reflections. Note: When fully describing a reflection, a mirror line must be added and discussed in the answer. - There can also be more than one mirror line e.g. Reflect the following object in mirror line m and n. m n Finding the mirror line. - The mirror line is ALWAYS half way between each point and its image AB C A’B’ C’DD’ A B A’ B’

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Rotation - To perform rotations a centre of rotation and an angle of rotation (or amount of turn) are needed - If not stated, the direction of a rotation is always anti-clockwise e.g. Rotate the object 90° clockwise about X clockwise about X A BC D X A’B’ C’D’ Properties: - Rotated lines, angles and areas remain the same size - Each point and its image are the same distance from the centre of rotation - The centre of rotation is invariant e.g. Rotate the object 270° about X about X A B CX A’ B’C’ Note: It can be a good idea using tracing paper and turning the paper about the centre of rotation

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e.g. Find the centre of rotation A A’ X To find the centre either: -Use tracing paper and guess location or -Find the intersection of the perpendicular bisectors of the lines joining a point to its image Note: When fully describing a rotation, a centre, angle and direction must be added and discussed in the answers Finding the centre of rotation

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Enlargement - To perform an enlargement, a centre and scale factor are needed 1. Scale Factor (s.f.) - To calculate the scale factor, use the following formula Scale factor (s.f.) = length of image length of object length of object e.g. Calculate the scale factor of the following enlargement A’ C’B’ A BC 6 9 3 Scale factor (s.f.) = 6 3 = 2 - The centre of enlargement is at the intersection of the lines joining points to their images e.g. Find the centre and scale factor of the following enlargement X Scale factor (s.f.) = 1 2 AA’ Centre = X 2. Centre of Enlargement

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3. Drawing Enlargements a) Using only the scale factor AA’ - Multiply lengths of the object by the s.f. and draw the image anywhere e.g. Enlarge the object by scale factor of 2 Remember when enlarging by only the scale factor, the image can be placed anywhere a) Using a centre and scale factor - Choose a point on the object and measure the distance between it and the centre - Multiply the distance by the scale factor and use it to plot a point of the image - Draw in the image making sure it is enlarged by the scale factor. e.g. Enlarge the object by scale factor of 2 and centre X A X A’ Properties: - Shape, sense and angle size remain the same - Lengths and areas change - The centre of enlargement is invariant Note: When fully describing an enlargement, a centre and scale factor must be added and discussed in the instructions

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- An object can also shrink with an enlargement! e.g. Enlarge the object by scale factor of -0.5 and centre X X A A’ - If the scale factor is -1 < x < 1 then the image will shrink. - If the scale factor is negative then the image ends up on the other side of the centre and reversed. e.g. Enlarge the object by scale factor of 0.5 and centre X A’ X A

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Translation - Is the movement of an object, without twisting, in a particular direction - The movement can be described by a vector or a direction e.g. Translate the object ‘A’ by the vector A Properties: - Translated lines, sense, angles and areas remain the same size A e.g. By what vector has the following object been translated? A’ A’ Vector = Note: When fully describing a translation, a vector or direction must be added and discussed in the answer - In a vector the top number describes sideways movement (negative = left) - The bottom number describes up/down movement (negative = down) - There are no invariant points

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