1. Transformations Objective: to develop an understanding of the four transformations. Starter – if 24 x 72 = 2016, find the value of: 1)2.8 x 72 = 2)2.8 x 7.2 = 3)0.28 x 7.2 = 201.6 20.16 2.016

2. What are the four types of transformations?

3. 1 2 3 4 5 6 7 8 9 -9 -8 -7 -6 -5 -4 -3 -2 -1 -2 -3 -4 -5 -6 -7 -8 -9 987654321987654321 x y 1 2 3 4 5 6 7 8 9 -9 -8 -7 -6 -5 -4 -3 -2 -1 -2 -3 -4 -5 -6 -7 -8 -9 987654321987654321 x y 1) Draw the line x = 1. Reflect the shape in the line you have drawn. 2) Draw the line x = 3. Reflect the shape in the line you have drawn. 1 2 3 4 5 6 7 8 9 -9 -8 -7 -6 -5 -4 -3 -2 -1 -2 -3 -4 -5 -6 -7 -8 -9 987654321987654321 x y 1 2 3 4 5 6 7 8 9 -9 -8 -7 -6 -5 -4 -3 -2 -1 -2 -3 -4 -5 -6 -7 -8 -9 987654321987654321 x y Reflection

4. 1 2 3 4 5 6 7 8 9 -9 -8 -7 -6 -5 -4 -3 -2 -1 -2 -3 -4 -5 -6 -7 -8 -9 987654321987654321 x y 1 2 3 4 5 6 7 8 9 -9 -8 -7 -6 -5 -4 -3 -2 -1 -2 -3 -4 -5 -6 -7 -8 -9 987654321987654321 x y 3) Draw the line x = y. Reflect the shape in the line you have drawn. 4) Draw the line x = y. Reflect the shape in the line you have drawn. 1 2 3 4 5 6 7 8 9 -9 -8 -7 -6 -5 -4 -3 -2 -1 -2 -3 -4 -5 -6 -7 -8 -9 987654321987654321 x y 1 2 3 4 5 6 7 8 9 -9 -8 -7 -6 -5 -4 -3 -2 -1 -2 -3 -4 -5 -6 -7 -8 -9 987654321987654321 x y Reflection

5. Describing Reflections 2 marks 1 mark for the type of transformation – reflection 2 nd mark for the mirror line (e.g. x = 1)

6. Vectors Vectors describe translations. They are represented as two numbers on top of each other in brackets. right up Right and up are positive numbers. left down Left and down are negative numbers.

7. Translation When an object is moved in a straight line in a given direction we say that it has been translated. For example, we can translate triangle ABC 5 squares to the right and 2 squares up: C A B object C A B C A B C A B C A B C A B C A B C A B C’C’ A’A’ B’B’ image Every point in the shape moves the same distance in the same direction. object

8. Translations on a coordinate grid 01234567–1–2–3–4–5–6–7 1 2 3 4 5 6 7 –2 –4 –6 –3 –5 –7 –1 Translate the shape 3 squares left and 8 squares down. Label each point in the image. A’(2, –1)B’(0, –6) C’(–5, –2) y x C(–2, 6) A(5, 7) B(3, 2)

9. Translations on a coordinate grid The coordinates of vertex A of this shape are (3, –4). When the shape is translated the coordinates of vertex A’ are(–3, 3). What translation will map the shape onto its image? 6 left 7 up 123456–2–3–4–5–6–7 1 2 5 6 –2 –4 –6 –3 –5 –7 –1 y x 7 3 4 7 0 A(3, –4) A’(–3, 3)

10. Describing Translations 2 marks 1 mark for the type of transformation – translation 2 nd mark for the vector (e.g. )

11. To enlarge the rectangle by scale factor x2 from the point shown. Centre of Enlargement Object A B C D Or Count Squares Image A/A/ B/B/ C/C/ D/D/ Enlargements from a Given Point 1. Draw the ray lines through vertices. 2. Mark off x2 distances along each line. 3. Draw and label image.

12. The small rectangle has been enlarged as shown. Find the centre of enlargement. Object A C D Image A/A/ B/B/ C/C/ D/D/ B Draw 2 ray lines through corresponding vertices to locate. Centre of Enlargement Finding the Centre of an Enlargement

13. Describing Enlargements 3 marks 1 mark for the type of transformation – enlargement 2 nd mark for the scale factor (e.g. x2) 3 rd mark for the centre of enlargement

14. Rotations on a coordinate grid The vertices of a triangle lie on the points A(2, 6), B(7, 3) and C(4, –1). 01234567–1–2–3–4–5–6–7 1 2 3 4 5 6 7 –2 –4 –6 –3 –5 –7 –1 A(2, 6) B(7, 3) C(4, –1) Rotate the triangle 180° clockwise about the origin and label each point on the image. A’(–2, –6) C’(–4, 1) What do you notice about each point and its image? B’(–7, –3)

15. Rotations on a coordinate grid 01234567–1–2–3–4–5–6–7 1 2 3 4 5 6 7 –2 –4 –6 –3 –5 –7 –1 A(–6, 7) B(2, 4) B’(–4, 2) Rotate the triangle 90° anticlockwise about the origin and label each point in the image. C(–4, 4) A’(–7, –6) C’(–4, –4)

16. Describing Rotations 3 marks 1 mark for the type of transformation – rotation 2 nd mark for the angle of turn and state whether its clockwise/anticlockwise (e.g. 90° clockwise) 3 rd mark for the centre of rotation (e.g. 0, 0)