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Maths Gcse Edexcel Higher

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  1. Scatter-Graphs-And-Correlation Edexcel Higher
    2 主题
  2. Cumulative-Frequency-And-Box-Plots Edexcel Higher
    4 主题
  3. Histograms Edexcel Higher
    3 主题
  4. Statistical-Diagrams Edexcel Higher
    7 主题
  5. Averages-Ranges-And-Data Edexcel Higher
    8 主题
  6. Combined-And-Conditional-Probability Edexcel Higher
    3 主题
  7. Tree-Diagrams Edexcel Higher
    1 主题
  8. Simple-Probability-Diagrams Edexcel Higher
    3 主题
  9. Transformations Edexcel Higher
    5 主题
  10. Vectors Edexcel Higher
    6 主题
  11. 3D-Pythagoras-And-Trigonometry Edexcel Higher
    1 主题
  12. Sine-Cosine-Rule-And-Area-Of-Triangles Edexcel Higher
    4 主题
  13. Pythagoras-And-Trigonometry Edexcel Higher
    4 主题
  14. Area-And-Volume-Of-Similar-Shapes Edexcel Higher
    1 主题
  15. Congruence-Similarity-And-Geometrical-Proof Edexcel Higher
    5 主题
  16. Volume-And-Surface-Area Edexcel Higher
    3 主题
  17. Circles-Arcs-And-Sectors Edexcel Higher
    2 主题
  18. Area-And-Perimeter Edexcel Higher
    4 主题
  19. Circle-Theorems Edexcel Higher
    7 主题
  20. Bearings-Scale-Drawing-Constructions-And-Loci Edexcel Higher
    5 主题
  21. Angles-In-Polygons-And-Parallel-Lines Edexcel Higher
    3 主题
  22. Symmetry-And-Shapes Edexcel Higher
    6 主题
  23. Exchange-Rates-And-Best-Buys Edexcel Higher
    2 主题
  24. Standard-And-Compound-Units Edexcel Higher
    5 主题
  25. Direct-And-Inverse-Proportion Edexcel Higher
    2 主题
  26. Problem-Solving-With-Ratios Edexcel Higher
    2 主题
  27. Ratios Edexcel Higher
    3 主题
  28. Sequences Edexcel Higher
    4 主题
  29. Transformations-Of-Graphs Edexcel Higher
    2 主题
  30. Graphing-Inequalities Edexcel Higher
    2 主题
  31. Solving-Inequalities Edexcel Higher
    2 主题
  32. Real-Life-Graphs Edexcel Higher
    4 主题
  33. Estimating-Gradients-And-Areas-Under-Graphs Edexcel Higher
    2 主题
  34. Equation-Of-A-Circle Edexcel Higher
    2 主题
  35. Graphs-Of-Functions Edexcel Higher
    6 主题
  36. Linear-Graphs Edexcel Higher
    4 主题
  37. Coordinate-Geometry Edexcel Higher
    4 主题
  38. Functions Edexcel Higher
    3 主题
  39. Forming-And-Solving-Equations Edexcel Higher
    3 主题
  40. Iteration Edexcel Higher
    1 主题
  41. Simultaneous-Equations Edexcel Higher
    2 主题
  42. Quadratic-Equations Edexcel Higher
    4 主题
  43. Linear-Equations Edexcel Higher
    1 主题
  44. Algebraic-Proof Edexcel Higher
    1 主题
  45. Rearranging-Formulas Edexcel Higher
    2 主题
  46. Algebraic-Fractions Edexcel Higher
    4 主题
  47. Completing-The-Square Edexcel Higher
    1 主题
  48. Factorising Edexcel Higher
    6 主题
  49. Expanding-Brackets Edexcel Higher
    3 主题
  50. Algebraic-Roots-And-Indices Edexcel Higher
    1 主题
  51. Introduction Edexcel Higher
    7 主题
  52. Using-A-Calculator Edexcel Higher
    1 主题
  53. Surds Edexcel Higher
    2 主题
  54. Rounding-Estimation-And-Bounds Edexcel Higher
    2 主题
  55. Fractions-Decimals-And-Percentages Edexcel Higher
    3 主题
  56. Simple-And-Compound-Interest-Growth-And-Decay Edexcel Higher
    4 主题
  57. Percentages Edexcel Higher
    3 主题
  58. Fractions Edexcel Higher
    4 主题
  59. Powers-Roots-And-Standard-Form Edexcel Higher
    4 主题
  60. Prime-Factors-Hcf-And-Lcm Edexcel Higher
    4 主题
  61. Number-Operations Edexcel Higher
    10 主题
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Exam code:1MA1

Rotations

What is a rotation?

  • A rotation turns a shape around a point

    • This is called the centre of rotation

  • The rotated image is the same size as the original image

    • It will have a new position and orientation

  • If the centre is a point on the original shape then that point is not changed by the rotation

    • It is called an invariant point

Clockwise & Anticlockwise

How do I rotate a shape?

  • STEP 1

    Place the tracing paper over page and draw over the original object

  • STEP 2

    Place the point of your pencil on the centre of rotation

  • STEP 3

    Rotate the tracing paper by the given angle in the given direction

    • The angle will be 90°, 180° or 270°

  • STEP 4
    Carefully draw the image onto the coordinate grid in the position shown by the tracing paper

How do I describe a rotation?

  • To describe a rotation, you must:

    • State that the transformation is a rotation

    • State the centre of rotation

    • State the angle of rotation 

      • This will be 90°, 180° or 270°

    • State the direction of rotation

      • Clockwise or anti-clockwise

      • A direction is not required if the angle is 180°

      • 90° clockwise is the same as 270° anti-clockwise

  • To find the centre of rotation:

    • If the rotation is 90° or 270°

      • Use tracing paper and start on the original shape

      • Try a point as the centre and rotate the original shape

      • If the rotated shape matches the image then that point is the centre

      • Otherwise keep picking points until one works

    • If the rotation is 180°

      • Draw lines connecting each vertex on the original shape with the corresponding vertices on the image

      • These lines will intersect at the centre of rotation

How do I reverse a rotation?

  • If a shape has been rotated to a new position, you can perform a single transformation to return the shape to its original position

  • A rotation can be reversed by simply reversing the direction of rotation

    • The angle of rotation is the same

    • The centre of rotation is the same

  • For a shape rotated by 45º in a clockwise direction about the point (0, 3)

    • The reverse transformation is

      • a rotation of 45º

      • in an anti-clockwise direction

      • about the point (0, 3)

Examiner Tips and Tricks

  • When you first go into the exam room, make sure there is some tracing paper on your desk ready for you

    • If there isn’t ask for some before the exam begins

  • Draw an arrow facing up on your tracing paper

    • The arrow will be facing left or right when you have turned 90° or 270°

    • The arrow will be facing down when you have turned 180°

  • Double-check that you have copied the rotated image into the correct position

    • Put the tracing paper over the original object and rotate it again to see that it lines up with your image

Worked Example

(a) On the grid below rotate shape A by 90° anti-clockwise about the point (0, 2).

Label your answer A’.

Shape to be rotated

Using tracing paper, draw over the original object and mark one vertex.
Mark on the centre of rotation.
Draw an arrow pointing vertically upwards on the paper.

Steps to rotate a shape

With your pencil fixed on the point of rotation, rotate the tracing paper 90o anti-clockwise, the arrow that you drew should now be pointing left.
Make a mental note of the new coordinates of the vertex that you marked on your tracing paper.
Draw the new position of this vertex onto the grid.

Steps to rotate a shape

Repeat this process for the other two vertices on the triangle.
Connect the vertices together to draw the rotated image.

Rotated shape

(b) Describe fully the single transformation that creates shape B from shape A.

Shape and its rotated image

You should be able to see that the object has been rotated 90o clockwise (or 270o anti-clockwise).
You are likely to be able to see roughly where the centre of rotation is but it may take a little time to find its position exactly.

<img alt=”Finding the centre of rotation” class=”ContentBlock_figure__vJw2q” data-nimg=”1″ decoding=”async” height=”1047″ loading=”lazy” sizes=”(max-width: 320px) 320w, (max-width: 640px) 640w, (max-width: 960px) 960w, (max-width: 1280px) 1280w, 1920w” src=”https://cdn.savemyexams.com/cdn-cgi/image/f=auto,width=3840/https://cdn.savemyexams.com/uploads/2020/03/Q2-Solution-Part-1.png” srcset=”https://cdn.savemyexams.com/cdn-cgi/image/f=auto,width=16/https://cdn.savemyexams.com/uploads/2020/03/Q2-Solution-Part-1.png 16w, https://cdn.savemyexams.com/cdn-cgi/image/f=auto,width=32/https://cdn.savemyexams.com/uploads/2020/03/Q2-Solution-Part-1.png 32w, https://cdn.savemyexams.com/cdn-cgi/image/f=a

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