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Flashcards · Maths

Transformations and Similarity

80 cards from 5 lessons

  1. What is a transformation?

    A change in the position, and sometimes the size, of a shape.

  2. What is the object and what is the image?

    The object is the original shape and the image is the shape after the transformation.

  3. What stays the same in a reflection?

    The size and shape, so the image is congruent to the object.

  4. How far is an image point from the mirror line?

    The same distance as the object point, on the other side.

  5. How do you describe a reflection fully?

    Say "reflection" and give the equation of the mirror line.

  6. What is the equation of the \(x\)-axis?

    \(y = 0\).

  7. What is the equation of the \(y\)-axis?

    \(x = 0\).

  8. What happens to the coordinates of a point reflected in the line \(y = x\)?

    They swap.

  9. What happens to the coordinates of a point reflected in the line \(y = -x\)?

    They swap and both change sign.

  10. What does a translation do?

    Slides every point the same distance in the same direction.

  11. What does the top number of a column vector show?

    The move to the right, or to the left if negative.

  12. What does the bottom number of a column vector show?

    The move up, or down if negative.

  13. How do you find a translation from a point and its image?

    Subtract the object coordinates from the image coordinates.

  14. Does a translation change the orientation of a shape?

    No, the shape faces the same way.

  15. Does a reflection change the orientation of a shape?

    Yes, it gives a mirror image.

  16. What should you write for "describe the transformation"?

    The name of the transformation and all of its details.

  17. What is a rotation?

    A turn of a shape through an angle about a fixed point.

  18. What is the centre of rotation?

    The point that stays fixed when a shape is rotated.

  19. What details describe a rotation?

    The centre, the angle and the direction.

  20. What are the common angles of rotation in a non-calculator exam?

    \(90^\circ\), \(180^\circ\) and \(270^\circ\).

  21. Why is no direction needed for a \(180^\circ\) rotation?

    Both directions give the same result.

  22. Where does \((x, y)\) go in a \(180^\circ\) rotation about the origin?

    \((-x, -y)\).

  23. Where does \((x, y)\) go in a \(90^\circ\) clockwise rotation about the origin?

    \((y, -x)\).

  24. Where does \((x, y)\) go in a \(90^\circ\) anticlockwise rotation about the origin?

    \((-y, x)\).

  25. How far is each point from the centre after a rotation?

    The same distance as before.

  26. How do you find the centre of a rotation?

    Find where the perpendicular bisectors of the lines joining points to their images cross.

  27. How can tracing paper help?

    Put the pencil on the centre and turn the paper to check the image.

  28. How do you find the centre of a \(180^\circ\) rotation?

    It is the midpoint of any point and its image.

  29. Is the image of a rotation the same size as the object?

    Yes, it is congruent.

  30. What is a quarter turn?

    A rotation of \(90^\circ\).

  31. What is a half turn?

    A rotation of \(180^\circ\).

  32. Which way is clockwise?

    The same way as the hands of a clock.

  33. What is an enlargement?

    A transformation that changes the size of a shape and keeps its angles.

  34. What is the scale factor?

    The number by which every length is multiplied.

  35. What is the centre of enlargement?

    The fixed point from which the distances are scaled.

  36. What happens to the angles in an enlargement?

    They stay the same.

  37. What is the scale factor if a side grows from 4 cm to 10 cm?

    \(\dfrac{10}{4} = 2.5\).

  38. What does a scale factor of \(\dfrac{1}{2}\) do to a shape?

    It halves every length, giving a smaller shape.

  39. How do you find the image of a point?

    Multiply its distance from the centre by the scale factor, in the same direction.

  40. How do you find the centre of an enlargement?

    Draw lines through each corner and its image and find where they meet.

  41. What do you give to describe an enlargement fully?

    The scale factor and the centre of enlargement.

  42. Is an enlarged shape congruent to the original?

    No, unless the scale factor is 1.

  43. Is an enlarged shape similar to the original?

    Yes, the shapes are similar.

  44. What is the image of \((2, 3)\) for scale factor 3 and centre the origin?

    \((6, 9)\).

  45. What does a negative scale factor do?

    It puts the image on the opposite side of the centre (Higher tier).

  46. Which transformation is an enlargement with scale factor \(-1\)?

    A rotation of \(180^\circ\) about the centre (Higher tier).

  47. How do you work out the scale factor from a side?

    Image length divided by object length.

  48. What are corresponding sides?

    Sides in the same position on the object and the image.

  49. What do two reflections in parallel lines give?

    A translation, at right angles to the lines.

  50. How far is the translation?

    Twice the distance between the mirror lines.

  51. What do two reflections in lines that cross give?

    A rotation about the point where the lines cross.

  52. What is the angle of that rotation?

    Twice the angle between the mirror lines.

  53. What single transformation is reflection in both axes?

    A rotation of \(180^\circ\) about the origin.

  54. Where does \((x, y)\) go after reflection in \(y = x\) then the \(x\)-axis?

    \((y, -x)\).

  55. What is an invariant point?

    A point that does not move under a transformation.

  56. Which points are invariant in a reflection?

    Every point on the mirror line.

  57. What is the invariant point of a rotation?

    The centre of rotation.

  58. Does a translation have an invariant point?

    No.

  59. How do you find the single transformation for a combination?

    Compare the first shape with the last.

  60. Why label each shape \(A\), \(B\) and \(C\)?

    It keeps the working clear and shows the order.

  61. Is the final image of a combination congruent to the object?

    Yes, if the transformations are reflections, rotations and translations.

  62. Does the order of two transformations always matter?

    Sometimes it does, so do them in the order given.

  63. What is the single transformation for two \(90^\circ\) clockwise rotations about the same centre?

    A rotation of \(180^\circ\) about that centre.

  64. What is a combined transformation?

    One transformation followed by another.

  65. What are congruent shapes?

    Shapes with exactly the same size and shape.

  66. What are similar shapes?

    Shapes with the same shape but not necessarily the same size.

  67. What are the conditions for congruent triangles?

    SSS, SAS, ASA and RHS.

  68. What does SSS mean?

    All three sides are equal.

  69. What does SAS mean?

    Two sides and the angle between them are equal.

  70. What does ASA mean?

    Two angles and a side are equal.

  71. What does RHS mean?

    A right angle, the hypotenuse and another side are equal.

  72. Why is AAA not enough for congruence?

    The triangles could be different sizes.

  73. What do you give in a congruence proof?

    Each equal pair with a reason, and the condition.

  74. What reasons can you use for equal sides or angles?

    Given, common side, vertically opposite angles, or alternate angles.

  75. How do you find the scale factor for similar shapes?

    Divide the length on one shape by the matching length on the other.

  76. If two angles of a triangle are equal to two of another, are the triangles similar?

    Yes, because the third angles are equal too.

  77. What is the area scale factor if the length scale factor is \(k\)?

    \(k^2\) (Higher tier).

  78. What is the volume scale factor if the length scale factor is \(k\)?

    \(k^3\) (Higher tier).

  79. Two similar shapes have areas in the ratio \(4 : 9\). What is the ratio of their lengths?

    \(2 : 3\) (Higher tier).

  80. What are corresponding sides?

    Sides in the same position on similar shapes.