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Transformation geometry

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CONTENTS

ITEM TYPE NUMBER
Transformations Workout 94 slides
Transformations Library 17 questions
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SAMPLE FROM THE WORKOUT

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SLIDE 1 - QUESITON 1

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SLIDE 2 - SOLUTION

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SAMPLE FROM THE LIBRARY

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QUESTION [difficulty 0.1]

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SOLUTION

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DEPENDENCIES

228: Working in three dimensions
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230: Transformation geometry
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232: Continuing algebra

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CONCEPTS

ITEM
 LEV.
Reflection / mirror symmetry 494.1
Line of symmetry 494.1
Axis of symmetry 494.5
Finite / infinite axes of symmetry 494.7
Symmetry problem in patterned figure 494.9
Problem of making symmetry in a patterned figure 495.1
Reflection, line of reflection 495.5
Reflection in x or y axis 495.7
Rotation 495.9
Rotational symmetry 495.9
Order of rotational symmetry 495.9
Rotation by 90 degrees - clockwise / anticlockwise 496.3
Centre of rotation is the origin 496.3
Rotation of a triangle by 90 degrees 496.5
Rotation of a line by 90 degrees 496.7
Rotation of a rectangle by 90 degrees 496.9
Rotation by 180 degrees 497.1
Result; rotation is two reflections 497.7
Rotation anticlockwise is 360 – rotation clockwise 498.1
Centre of rotation other than origin 498.3
Finding the centre of 180 degree rotation 499.1
Finding the centre of 90 degree rotation 499.5
Finding line of reflection 499.9
Order of reflective symmetry 500.3
Doubling dimensions of plane figure 500.7
Area of plane figure with doubled sides 500.7
Enlargement 500.9
Enlargment from a corner 501.2
Centre of enlargement 501.5
Scale factor 501.5
Finding centre of enlargement 502.3
Scale factor less than 1 502.7
Negative scale factor 503.1

RAW CONTENT OF THE WORKOUT

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SLIDE 3 How many lines of symmetry do the above have? Mark the lines of symmetry onto the diagrams. SLIDE 4 Equilateral triangles have 3 lines of symmetry Isosceles triangles have 1 line of symmetry General scalene triangles have 0 lines of symmetry SLIDE 5 Mark the axes of symmetry of the regular hexagon and regular pentagon SLIDE 6 The regular hexagon has 6 axes of symmetry The regular pentagon has 5 axes of symmetry SLIDE 7 How many axes of symmetry does ? a circle and ? a rectangle have? SLIDE 8 ? Every diameter of a circle is an axis of symmetry. Therefore, the circle has infinitely many axes of symmetry. ? The rectangle has 2 axes of symmetry. SLIDE 9 In each case find all the lines of symmetry and state how many there are. SLIDE 10 SLIDE 11 Shade in two more squares so that the figure has one axis of symmetry. SLIDE 12 SLIDE 13 A square has 4 lines of symmetry. How many squares must be shaded to in the left hand diagram to obtain a figure with each of the lines of symmetry? SLIDE 14 2 squares for symmetries 1 and 3 3 squares for symmetry 4 4 squares for symmetry 2 SLIDE 15 To reflect an object means to draw its mirror image Reflect the above object by drawing its mirror image on the other side of the line of reflection SLIDE 16 SLIDE 17 Plot the shape with coordinates whose vertices are Label the shape A. Reflect A in the y-axis and label the shape B. Reflect A in the x-axis and label the shape C. SLIDE 18 SLIDE 19 Draw what you see if you progressively rotate a square about its centre through . How many times does the square fit exactly into its original position? This number of times that the square matches its own shape is called the order of its rotational symmetry. What is the order of the rotational symmetry of the square? SLIDE 20 The order of the rotational symmetry of the square is 4 SLIDE 21 The rotational symmetries of the square are When we get to this is the original position Question What are the rotational symmetries of the equilateral triangle and the regular hexagon? SLIDE 22 Equilateral triangle Order of rotational symmetry is 3 The rotational symmetries are Hexagon Order of rotational symmetry is 7 The rotational symmetries are SLIDE 23 Rotate the red line segment clockwise by 90° about the origin, where the two axes meet. SLIDE 24 SLIDE 25 ? Write onto the diagram the coordinates of A ? Write onto the diagram the length of the height and base of the triangle ? Rotate the triangle 90° clockwise about the origin ? Write onto the diagram the coordinates of the point to which A has been moved by the clockwise rotation of 90° SLIDE 26 SLIDE 27 Rotate the line AB by 90° clockwise about the origin. Mark the new line A´B´. SLIDE 28 SLIDE 29 Rotate ABCD by 90° clockwise about the origin. Mark the position of the new object A´B´C´D´. SLIDE 30 SLIDE 31 ? Write onto the diagram the coordinates of A ? Write onto the diagram the length of the height and base of the triangle ? Rotate the triangle 180° clockwise about the origin ? Write onto the diagram the coordinates of the point to which A has been moved by the clockwise rotation of 180° SLIDE 32 SLIDE 33 A rotation by 180° is the same as a reflection through the origin. Rotate the object by 180° clockwise about the origin. SLIDE 34 SLIDE 35 Rotate the object about the origin ? 90° clockwise, ? 180° clockwise SLIDE 36 SLIDE 37 ? Rotate the object 180° clockwise about the origin ? On a separate diagram, reflect the object firstly in the y-axis, and then reflect that object in the x-axis ? What do you notice about the effect of ? and ?? SLIDE38 The double reflection produces the same result as the rotation by 180°. This is always true. A rotation is result of two reflections. SLIDE 39 Rotate the object 90° anticlockwise about the origin SLIDE 40 SLIDE 41 Complete the following table Rotation clockwise Rotation anticlockwise 90° 180° 45° 225° 360° 0° 60° 240° 330° SLIDE 42 Rotation clockwise Rotation anticlockwise 90° 270° 180° 180° 45° 315° 135° 225° 360° 360° 0° 0° 60° 300° 120° 240° 30° 330° SLIDE 43 Rotate the object 90° clockwise about the centre SLIDE 44 SLIDE 45 Rotate the object 90° clockwise about SLIDE 46 SLIDE 47 Rotate the object 180° clockwise about SLIDE 48 SLIDE 49 Reflect the object in both the red and the blue lines SLIDE 50 SLIDE 51 The object has been rotated 180°. Find its centre of rotation. SLIDE 52 The centre of the rotation is SLIDE 53 The object has been rotated 180°. Find its centre of rotation. SLIDE 54 The centre of the rotation is SLIDE 55 The object has been rotated clockwise by 90° Find its centre of rotation SLIDE 56 The centre of the rotation is SLIDE 57 The object has been rotated anticlockwise by 90° Find its centre of rotation SLIDE 58 The centre of the rotation is SLIDE 59 The two objects are mirror images of each other. Draw in the line of reflection. SLIDE 60 SLIDE 61 The two objects are mirror images of each other. Draw in the line of reflection. SLIDE 62 SLIDE 63 Recall that the order of reflective symmetry of an object is the number of lines in which the object may be divided into two halves that are mirror images of each other. Find the order of symmetry of each of the following letters? SLIE 64 SLIDE 65 Which of the following has an order of reflective symmetry of 1? SLIDE 66 There are three letters, A, C and E that have order of symmetry 1. The letter B is not symmetrical about the central line because the upper part is smaller than the lower part. SLIDE 67 Draw in the space below a rectangle whose length is double the length and width of the rectangle shown. What is the area of each rectangle? How many times bigger is the area of the larger rectangle to the smaller rectangle? SLIDE 68 The area of the larger rectangle is times the area of the smaller rectangle. The ratio is SLIDE 69 Enlarge the square three times about its centre. How many times larger is the enlarged square than the original square? SLIDE 70 The larger square is 9 times larger than the smaller square. SLIDE 71 Enlarge the rectangle four times about the corner marked. How many times larger is the new rectangle to the old? SLIDE 72 The larger rectangle is 16 times larger than the smaller rectangle SLIDE 73 Complete this table Enlargement of length and width Enlargement of area 2 3 4 5 6 n SLIDE 74 Enlargement of length and width Enlargement of area 2 3 4 5 6 n SLIDE 75 Enlarge the object by scale factor 3 from the centre of enlargement point shown. SLIDE 76 SLIDE 77 Enlarge the object by scale factor 5 from the centre of enlargement point shown. SLIDE 78 SLIDE 79 Enlarge the object by scale factor 2 where the centre of enlargement is the origin . SLIDE 80 SLIDE 81 Enlarge the object by scale factor 3 where the centre of enlargement is . SLIDE 82 SLIDE 83 Find the coordinate of the centre of enlargement SLIDE 84 The coordinates of the centre of enlargement are SLIDE 85 Find the centre of enlargement SLIDE 86 The centre of enlargement is SLIDE 87 Scale the object by factor . P is the centre for the scaling. SLIDE 88 To scale by a factor less than 1 is to shrink the object SLIDE 89 Scale the object by a factor of centre SLIDE 90 SLIDE 91 Scale the object through the origin by factor SLIDE 92 A scaling by a negative factor is both a reflection and a scaling SLIDE 93 Scale the object by scale factor through the origin SLIDE 94