[discia] GCSE Maths › Geometry & Measures › Enlarging with Negative Scale Factors

Enlarging with Negative Scale Factors

discia.org 10 questions · 29 marks
Name Date
  1. Either paper 2 marks

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

    Draw the image on the grid.

    Show answer
    The image is the triangle with vertices \((-2, -1)\), \((-8, -1)\) and \((-2, -10)\)
    -9-8-7-6-5-4-3-2123456789-11-10-9-8-7-6-5-4-3-212345670xyA
    Another like this
  2. Either paper 4 marks

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

    -4-3-2123456789101234567890xyA
    (a)

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

    Draw shape B on the grid.

    (b)

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

    Show answer
    (a) B is the triangle with vertices \((0, 2)\), \((-3, 2)\) and \((0, 0)\)
    (b) Rotation of \(180^\circ\) about \((3, 4)\)
    (a)-4-3-2123456789101234567890xyAB
    Another like this
  3. Either paper 3 marks

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

    Show answer
    (a) \((-8, 0)\)
    (b) \(-\frac{1}{ 2 }\)
    Another like this
  4. Either paper 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.

    -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.

    Show answer
    (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.
    Another like this
  5. Either paper 2 marks

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

    -3-21234567891011-3-212345678910110xyA

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

    Draw the image on the grid.

    Show answer
    The image is the triangle with vertices \((0, 1)\), \((-2, 1)\) and \((0, -2)\)
    -3-21234567891011-3-212345678910110xyA
    Another like this
  6. Either paper 3 marks

    Shapes A and B are drawn on the grid.

    -10-8-6-4-22468-6-5-4-3-2123456780xyAB

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

    Show answer
    Enlargement, scale factor \(-2\), centre \((2, 3)\)
    Another like this
  7. Either paper 2 marks

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

    Draw the image on the grid.

    Show answer
    The image is the triangle with vertices \((-1, -4)\), \((-7, -4)\) and \((-1, -8)\)
    -8-7-6-5-4-3-2123456789-9-8-7-6-5-4-3-2123456780xyA
    Another like this
  8. Either paper 4 marks

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

    -212345678-3-2-11234567890xyA
    (a)

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

    Draw shape B on the grid.

    (b)

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

    Show answer
    (a) B is the triangle with vertices \((1, 1)\), \((-1, 1)\) and \((1, -2)\)
    (b) Rotation of \(180^\circ\) about \((3, 3)\)
    (a)-212345678-3-2-11234567890xyAB
    Another like this
  9. Either paper 3 marks

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

    Show answer
    (a) \((-4, -2)\)
    (b) \(-\frac{1}{ 2 }\)
    Another like this
  10. Either paper 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.

    -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.

    Show answer
    (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.
    Another like this
discia.org Enlarging with Negative Scale Factors · sheet 1
Answers Enlarging with Negative Scale Factors · sheet 1
  1. The image is the triangle with vertices \((-2, -1)\), \((-8, -1)\) and \((-2, -10)\)
    -9-8-7-6-5-4-3-2123456789-11-10-9-8-7-6-5-4-3-212345670xyA
  2. (a) B is the triangle with vertices \((0, 2)\), \((-3, 2)\) and \((0, 0)\)
    (b) Rotation of \(180^\circ\) about \((3, 4)\)
    (a)-4-3-2123456789101234567890xyAB
  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 \((0, -2)\)
    -3-21234567891011-3-212345678910110xyA
  6. Enlargement, scale factor \(-2\), centre \((2, 3)\)
  7. The image is the triangle with vertices \((-1, -4)\), \((-7, -4)\) and \((-1, -8)\)
    -8-7-6-5-4-3-2123456789-9-8-7-6-5-4-3-2123456780xyA
  8. (a) B is the triangle with vertices \((1, 1)\), \((-1, 1)\) and \((1, -2)\)
    (b) Rotation of \(180^\circ\) about \((3, 3)\)
    (a)-212345678-3-2-11234567890xyAB
  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.
discia.org Enlarging with Negative Scale Factors · sheet 1