[discia] GCSE Maths › Geometry & Measures › Transformations

Transformations

discia.org 10 questions · 19 marks
Name Date
  1. Either paper 2 marks

    Shape A is drawn on the grid.

    -5-4-3-2-112345-5-4-3-2-1123450xyA

    Reflect shape A in the y-axis.

    Draw the image on the grid.

    Show answer
    The image is the triangle with vertices \((1, -2)\), \((3, -2)\) and \((1, -4)\)
    -5-4-3-2-112345-5-4-3-2-1123450xyA
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  2. Either paper 2 marks

    Shape A is drawn on the grid.

    -2-11234567-1123456789100xyA55

    Translate shape A by the vector \(\begin{pmatrix} 5 \\ 5 \end{pmatrix}\).

    Draw the image on the grid.

    Show answer
    Every corner moves 5 right and 5 up; the corner \((-1, 2)\) lands on \((4, 7)\)
    -2-11234567-1123456789100xyA55
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  3. Either paper 1 mark

    A shape is translated by the vector \(\begin{pmatrix} 5 \\ 0 \end{pmatrix}\).

    In which direction does the shape move?

    Circle your answer.

    up      down      left      right

    Show answer
    right
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  4. Either paper 2 marks

    Shape A and the line \(x = -1\) are drawn on the grid.

    -7-6-5-4-3-212345-2-1123450xyAx = -1

    Reflect shape A in the line \(x = -1\).

    Draw the image on the grid.

    Show answer
    The image has vertices \((1, 0)\), \((4, 0)\), \((4, 2)\) and \((1, 3)\)
    -7-6-5-4-3-212345-2-1123450xyAx = -1
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  5. Either paper 2 marks

    Shape A is drawn on the grid.

    -6-5-4-3-2123456-6-5-4-3-2-11234560xyA90° clockwise

    Rotate shape A through \(90^\circ\) clockwise about the origin.

    Draw the image on the grid.

    Show answer
    The image has vertices \((1, -1)\), \((1, -3)\), \((2, -3)\) and \((5, -1)\)
    -6-5-4-3-2123456-6-5-4-3-2-11234560xyA90° clockwise
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  6. Either paper 2 marks

    Shapes A and B are drawn on the grid.

    -112345678-5-4-3-2-11230xyAB

    Describe fully the single transformation that maps shape A onto shape B.

    Show answer
    Translation by the vector \(\begin{pmatrix} 3 \\ -4 \end{pmatrix}\)
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  7. Either paper 2 marks

    Shape A and the line \(y = -x\) are drawn on the grid.

    -6-5-4-3-2123456-6-5-4-3-2-11234560xyAy = -x

    Reflect shape A in the line \(y = -x\).

    Draw the image on the grid.

    Show answer
    The image is the triangle with vertices \((2, -3)\), \((2, -5)\) and \((-1, -3)\)
    -6-5-4-3-2123456-6-5-4-3-2-11234560xyAy = -x
    Another like this
  8. Either paper 2 marks

    Shape A is drawn on the grid. The centre of rotation \((2, -1)\) is marked with a cross.

    -4-3-212345678-5-4-3-2-11230xyA

    Rotate shape A through \(180^\circ\) about \((2, -1)\).

    Draw the image on the grid.

    Show answer
    The image is the triangle with vertices \((0, -2)\), \((-3, -2)\) and \((0, -4)\)
    -4-3-212345678-5-4-3-2-11230xyA
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  9. Either paper 2 marks

    Shape A is drawn on the grid. The centre of enlargement \((-1, -1)\) is marked with a cross.

    -2-11234-2-1123456780xyAscale factor 2

    Enlarge shape A by scale factor 2, centre \((-1, -1)\).

    Draw the image on the grid.

    Show answer
    The image is the triangle with vertices \((1, 3)\), \((3, 3)\) and \((1, 7)\)
    -2-11234-2-1123456780xyAscale factor 2
    Another like this
  10. Either paper 2 marks

    Shapes A and B are drawn on the grid.

    -2-112345-4-3-2-11234560xyAB

    Describe fully the single transformation that maps shape A onto shape B.

    Show answer
    Reflection in the line \(y = 1\)
    Another like this
discia.org Transformations · sheet 1
Answers Transformations · sheet 1
  1. The image is the triangle with vertices \((1, -2)\), \((3, -2)\) and \((1, -4)\)
    -5-4-3-2-112345-5-4-3-2-1123450xyA
  2. Every corner moves 5 right and 5 up; the corner \((-1, 2)\) lands on \((4, 7)\)
    -2-11234567-1123456789100xyA55
  3. right
  4. The image has vertices \((1, 0)\), \((4, 0)\), \((4, 2)\) and \((1, 3)\)
    -7-6-5-4-3-212345-2-1123450xyAx = -1
  5. The image has vertices \((1, -1)\), \((1, -3)\), \((2, -3)\) and \((5, -1)\)
    -6-5-4-3-2123456-6-5-4-3-2-11234560xyA90° clockwise
  6. Translation by the vector \(\begin{pmatrix} 3 \\ -4 \end{pmatrix}\)
  7. The image is the triangle with vertices \((2, -3)\), \((2, -5)\) and \((-1, -3)\)
    -6-5-4-3-2123456-6-5-4-3-2-11234560xyAy = -x
  8. The image is the triangle with vertices \((0, -2)\), \((-3, -2)\) and \((0, -4)\)
    -4-3-212345678-5-4-3-2-11230xyA
  9. The image is the triangle with vertices \((1, 3)\), \((3, 3)\) and \((1, 7)\)
    -2-11234-2-1123456780xyAscale factor 2
  10. Reflection in the line \(y = 1\)
discia.org Transformations · sheet 1