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Enlarging with Negative Scale Factors 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 29 marks Sheet 1
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  1. 2 marks

    Shape A is drawn on the grid. The centre of enlargement \((4, 2)\) is marked with a cross.

    A small triangle labelled A on a squared grid, with the centre of enlargement marked by a cross-9-8-7-6-5-4-3-2123456789-11-10-9-8-7-6-5-4-3-212345670xyA

    Enlarge shape A by scale factor \(-3\), centre \((4, 2)\).

  2. 4 marks

    Shape A is drawn on the grid. The point \((3, 4)\) is marked with a cross.

    A triangle labelled A on a squared grid, with the centre of enlargement marked by a cross-4-3-2123456789101234567890xyA
    (a)

    Enlarge shape A by scale factor \(-1\), centre \((3, 4)\). Label the image B.

    (b)

    Describe fully a different single transformation that also maps shape A onto shape B.

  3. 3 marks

    Shape A is drawn on the grid. The centre of enlargement \((2, 4)\) is marked with a cross.

    A triangle labelled A on a squared grid, with the centre of enlargement marked by a cross-9-8-7-6-5-4-3-212345678-5-4-3-21234567890xyA

    Shape A is enlarged by scale factor \(-2\), centre \((2, 4)\), to give shape B.

    (a)

    Write down the coordinates of the image of the vertex of shape A at \((7, 6)\).

    (b)

    State the scale factor of the single enlargement that maps shape B back onto shape A.

  4. 3 marks

    Shape A has been enlarged to give shape B. The centre of enlargement is marked with a cross at \((2, 2)\), and the dashed lines join each corner of A to the matching corner of B.

    Triangle A and its image B on opposite sides of a marked centre of enlargement, with dashed rays drawn through the centre to each pair of matching corners-10-8-6-4-2246-8-7-6-5-4-3-21234560xyAB
    (a)

    Write down the scale factor of the enlargement.

    (b)

    Explain how the diagram shows that the scale factor is negative.

  5. 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-3-21234567891011-3-212345678910110xyA

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

  6. 3 marks

    Shapes A and B are drawn on the grid.

    Two triangles labelled A and B on a squared grid, one larger than the other and the other way up-10-8-6-4-22468-6-5-4-3-2123456780xyAB

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

  7. 2 marks

    Shape A is drawn on the grid. The centre of enlargement \((3, 2)\) is marked with a cross.

    A small triangle labelled A on a squared grid, with the centre of enlargement marked by a cross-8-7-6-5-4-3-2123456789-9-8-7-6-5-4-3-2123456780xyA

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

  8. 4 marks

    Shape A is drawn on the grid. The point \((3, 3)\) is marked with a cross.

    A triangle labelled A on a squared grid, with the centre of enlargement marked by a cross-212345678-3-2-11234567890xyA
    (a)

    Enlarge shape A by scale factor \(-1\), centre \((3, 3)\). Label the image B.

    (b)

    Describe fully a different single transformation that also maps shape A onto shape B.

  9. 3 marks

    Shape A is drawn on the grid. The centre of enlargement \((4, 4)\) is marked with a cross.

    A triangle labelled A on a squared grid, with the centre of enlargement marked by a cross-5-4-3-2123456789-7-6-5-4-3-2123456789100xyA

    Shape A is enlarged by scale factor \(-2\), centre \((4, 4)\), to give shape B.

    (a)

    Write down the coordinates of the image of the vertex of shape A at \((8, 7)\).

    (b)

    State the scale factor of the single enlargement that maps shape B back onto shape A.

  10. 3 marks

    Shape A has been enlarged to give shape B. The centre of enlargement is marked with a cross at \((2, 2)\), and the dashed lines join each corner of A to the matching corner of B.

    Triangle A and its image B on opposite sides of a marked centre of enlargement, with dashed rays drawn through the centre to each pair of matching corners-14-12-10-8-6-4-22468-14-12-10-8-6-4-224680xyAB
    (a)

    Write down the scale factor of the enlargement.

    (b)

    Explain how the diagram shows that the scale factor is negative.

Answers

  1. The image is the triangle with vertices \((-2, -1)\), \((-8, -1)\) and \((-2, -10)\)
  2. (a) B is the triangle with vertices \((0, 2)\), \((-3, 2)\) and \((0, 0)\)
    (b) Rotation of \(180^\circ\) about \((3, 4)\)
  3. (a) \((-8, 0)\)
    (b) \(-\frac{1}{ 2 }\)
  4. (a) \(-3\)
    (b) Each dashed line passes through the marked centre at \((2, 2)\), with A on one side of it and B on the other, so the image is the opposite way round from the object.
  5. The image is the triangle with vertices \((0, 1)\), \((-2, 1)\) and \((0, -2)\)
  6. Enlargement, scale factor \(-2\), centre \((2, 3)\)
  7. The image is the triangle with vertices \((-1, -4)\), \((-7, -4)\) and \((-1, -8)\)
  8. (a) B is the triangle with vertices \((1, 1)\), \((-1, 1)\) and \((1, -2)\)
    (b) Rotation of \(180^\circ\) about \((3, 3)\)
  9. (a) \((-4, -2)\)
    (b) \(-\frac{1}{ 2 }\)
  10. (a) \(-3\)
    (b) Each dashed line passes through the marked centre at \((2, 2)\), with A on one side of it and B on the other, so the image is the opposite way round from the object.

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