Discia GCSE Maths › Geometry & Measures › Transformations

Transformations worksheet

10 GCSE practice questions with answers, free to print. Every sheet is generated, so you can make a fresh one whenever you need it.

10 questions 20 marks Sheet 1
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  1. 2 marks

    Shape A is drawn on the grid.

    A right-angled triangle labelled A on a squared grid-5-4-3-2-112345-5-4-3-2-1123450xyA

    Reflect shape A in the y-axis.

  2. 2 marks

    Shape A is drawn on the grid.

    An L-shape labelled A on a squared grid, with an arrow showing the translation-2-11234567-1123456789100xyA55

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

  3. 2 marks

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

    A trapezium labelled A on a squared grid, with a dashed mirror line-7-6-5-4-3-212345-4-3-2-112340xyAx = -1

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

  4. 2 marks

    Shape A is drawn on the grid.

    A trapezium labelled A on a squared grid, with the centre of rotation marked at the origin-6-5-4-3-2123456-6-5-4-3-2-11234560xyA90° clockwise

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

  5. 2 marks

    Shapes A and B are drawn on the grid.

    Two identical trapeziums labelled A and B on a squared grid-4-3-2-11234567-6-5-4-3-2-1120xyAB

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

  6. 2 marks

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

    A triangle labelled A on a squared grid, with a dashed diagonal mirror line-5-4-3-2-112345-5-4-3-2-1123450xyAy = -x

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

  7. 2 marks

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

    A triangle labelled A on a squared grid, with the centre of rotation marked by a cross-6-5-4-3-2-11234-3-2-112345670xyA

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

  8. 2 marks

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

    A small triangle labelled A on a squared grid, with the centre of enlargement marked by a cross-3-2-112345-3-2-1123456780xyAscale factor 3

    Enlarge shape A by scale factor 3, centre \((-2, -2)\).

  9. 2 marks

    Shapes A and B are drawn on the grid.

    Two congruent trapeziums labelled A and B on a squared grid-5-4-3-2-1123-7-6-5-4-3-2-11230xyAB

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

  10. 2 marks

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

    A triangle labelled A on a squared grid, with the centre of enlargement marked by a cross-3-2-112345-3-2-112345670xyA

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

Answers

  1. The image is the triangle with vertices \((1, -2)\), \((3, -2)\) and \((1, -4)\)
  2. Every corner moves 5 right and 5 up; the corner \((-1, 2)\) lands on \((4, 7)\)
  3. The image has vertices \((-3, -2)\), \((-6, -2)\), \((-6, -1)\) and \((-3, 2)\)
  4. The image has vertices \((1, -1)\), \((1, -4)\), \((2, -4)\) and \((5, -1)\)
  5. Translation by the vector \(\begin{pmatrix} -5 \\ -4 \end{pmatrix}\)
  6. The image is the triangle with vertices \((1, -2)\), \((1, -4)\) and \((-1, -2)\)
  7. The image is the triangle with vertices \((-2, 1)\), \((-5, 1)\) and \((-2, -2)\)
  8. The image is the triangle with vertices \((1, 4)\), \((4, 4)\) and \((1, 7)\)
  9. Reflection in the line \(y = -2\)
  10. The image is the triangle with vertices \((0, 0)\), \((1, 0)\) and \((0, 2)\)

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