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The three diagrams A , B and C show an object and its image under a certain transformation.

Explore 3 diagrams showing objects and their images under various transformations. Identify transformations including rotation, translation, axial symmetry, and central symmetry.

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The three diagrams A , B and C show an object and its image under a certain transformation.

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  1. 1. The three diagrams A, B and Cshow an object and its image under a certain transformation. For each of A, B and C, state one transformation (translation, axial symmetry or central symmetry) that will map the object onto that image. A– Axial symmetry B– Translation C– Central symmetry in O or a rotation of 180o about O

  2. 2. During a PE class the teacher, Mr Burke moves a gym mat using the following transformations one after another: 1. Rotation of 90° clockwise about the point C. 2. Translation of 8 units right and 6 units up. 3. Axial symmetry in the line AB. Copy the grid shown and show the final location of the mat.

  3. 3. (i) What is the image of G under a 90° anticlockwise rotation about O? E (ii) What is the image of E under axial symmetry in the line GC? A

  4. 3. (iii) If F is rotated 270° clockwise about O, which point will it go to? D (iv) Describe a transformation that will make F the image of B. Central symmetry in O or 180° rotation about O or axial symmetry in [HD]

  5. 3. (v) Describe the rotation that would move H to F. 90° anticlockwise rotation about O or axial symmetry in [GC]

  6. 4. Copy the diagram and enlarge the triangle ABC using a scale factor of 3·5 and a centre of enlargement . Steps: 1. Measure |OA| 2. Multiply |OA| by 3·5 3. Draw a line from O through A length = 3·5 |OA| 4. Repeat for B and C. 5. Join points to make image

  7. 5. The diagram shows a regular hexagon. (i) How many axes of symmetry has the hexagon? 6

  8. 5. The diagram shows a regular hexagon. (ii) Copy the diagram into your copy and draw in the axes of symmetry.

  9. 5. The diagram shows a regular hexagon. (iii) [AD] and [CF] intersect at O. What is the measure of the angle of the rotation, about O, which maps A onto C? 120° anticlockwise rotation or 240° clockwise rotation Explanation hexagon has 6 segments segment

  10. 5. The diagram shows a regular hexagon. (iv) Describe one transformation which maps [AF] to [CD]. Translation

  11. 6. Each of the pictures labelledA, B and C shown below is the image of the figure shown on the right, under a transformation. For each of A, B and C, state what the transformation is (translation, central symmetry, axial symmetry or rotation) and in the case of a rotation, state the angle. A– Rotation: 90° anticlockwise or 270° clockwise B– Central symmetry C– Axial symmetry

  12. 7. Describe the transformation shown in A, B, C and D below. A– Central symmetry B– Axial symmetry C– Translation D– Axial symmetry in a slanted line

  13. 8. A ferris wheel is an example of a rotation. The ferris wheel shown has 20 cars. (i) What is the measure of the angle of rotation if seat 1 of this ferris wheel is moved to the seat 5 position. Full circle = 360° Circle is divided into 20 sections Each section Each section = 18° To rotate seat 1 to seat 5 means to move it 4 sections 4  18 = 72

  14. 8. A ferris wheel is an example of a rotation. The ferris wheel shown has 20 cars. (ii) If seat 1 in the diagram is rotated 144°, find the seat position in the diagram that it now occupies. Seat 1 has moved eight positions/sections to Seat 9

  15. 9. EFGH is a square and EFHX is a parallelogram. Under the translation what is the image of: (i) ΔEXH ΔFHG (ii) [EH] [FG]

  16. 9. EFGH is a square and EFHX is a parallelogram. Under the translation what is the image of: (iii) EXH FHG

  17. 9. EFGH is a square and EFHX is a parallelogram. Under the translation what is the image of: (iv) ΔFHG ΔEXH (v) [FH] [EX]

  18. 9. EFGH is a square and EFHX is a parallelogram. Under the translation what is the image of: (vi) GFH HEX

  19. 9. EFGH is a square and EFHX is a parallelogram. Name a translation equal to: (vii) (ix) (viii)

  20. 10. The diagram shows a quadrilateral, A, and its image under different transformations. Write down the coordinates of the vertices of A under: (i) axial symmetry in the y-axis. (−1, 1) (−1, 4) (−4, 1) (−5, 5)

  21. 10. The diagram shows a quadrilateral, A, and its image under different transformations. Write down the coordinates of the vertices of A under: (ii) central symmetry in the point (0, 0). (−1, −1) (−4, −1) (−1, −4) (−5, −5)

  22. 10. The diagram shows a quadrilateral, A, and its image under different transformations. Write down the coordinates of the vertices of A under: (iii) axial symmetry in the x-axis. (1, −1) (1, −4) (4, −1) (5, −5)

  23. 11. The diagram shows a shape that has undergone several transformations. Describe the single transformation that maps: (i) A1 to A2 Axial symmetry in the y axis

  24. 11. The diagram shows a shape that has undergone several transformations. Describe the single transformation that maps: (ii) A1 to A3 Central symmetry in one point (0, 0)

  25. 11. The diagram shows a shape that has undergone several transformations. Describe the single transformation that maps: (iii) A1 to A4 Translation – 6 down, 2 across

  26. 11. The diagram shows a shape that has undergone several transformations. Describe the single transformation that maps: (iv) A2 to A3 Axial symmetry in the x axis

  27. 12. Triangle XYZ is the image of triangle ABC under enlargement, with centreO. |AB| = 6 and |XZ| = 18. The scale factor is 1·5. (i) Find |XY|. Scale factor = 1·5 given |AB| = 6 given Object = ΔABC 6  1·5 = Multiply both sides by 6 Image = ΔXYZ 9 = |XY |

  28. 12. Triangle XYZ is the image of triangle ABC under enlargement, with centreO. |AB| = 6 and |XZ| = 18. The scale factor is 1·5. (ii) Find |AC|. Scale factor = Scale factor = 1·5 given = 18 Object = ΔABC Image = ΔXYZ 1·5  |AC| = multiply both sides by

  29. 12. Triangle XYZ is the image of triangle ABC under enlargement, with centreO. |AB| = 6 and |XZ| = 18. The scale factor is 1·5. (ii) Find |AC|. Divide both sides by 1·5 Object = ΔABC Image = ΔXYZ

  30. 12. Triangle XYZ is the image of triangle ABC under enlargement, with centreO. |AB| = 6 and |XZ| = 18. The scale factor is 1·5. (iii) If the area of triangle ABC is 31·2 square units, calculate the area of triangle XYZ. (Scale factor)2 = Scale factor = 1·5 Area ΔABC = 31·2 Square units Object = ΔABC Image = ΔXYZ (1·5)2 = 2·25  31·2 = 70·2 square units = area ΔXYZ

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