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Exam questions · Maths · Transformations and Similarity

Enlargements

  • 6 exam questions
  • 17 marks
  • 9 quick checks
  1. 1 Write down [2 marks]

    A line is 7 cm long. It is enlarged by a scale factor of 3. Write down the length of the enlarged line. [2 marks]

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    Model answer

    \(7 \times 3 = 21\) cm.

    Mark scheme

    • \(7 \times 3\) — M1
    • 21 cm — A1
  2. 2 Enlarge [3 marks]

    Enlarge triangle \(T\) by a scale factor of \(\dfrac{1}{2}\) with the centre \(O\), the origin. [3 marks]

    Triangle T on a grid with the centre of enlargement O at the origin.
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    Model answer

    Multiply each coordinate by \(\dfrac{1}{2}\): \((2, 2)\) goes to \((1, 1)\), \((6, 2)\) goes to \((3, 1)\) and \((2, 4)\) goes to \((1, 2)\).

    Mark scheme

    • Enlarges at least two vertices by a scale factor of \(\dfrac{1}{2}\) — M1
    • At least two vertices correct — A1
    • Triangle with vertices \((1, 1)\), \((3, 1)\) and \((1, 2)\) — A1
  3. 3 Describe [3 marks]

    Describe fully the single transformation that maps triangle \(A\) onto triangle \(B\). [3 marks]

    Triangle A and its larger image triangle B on a grid.
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    Model answer

    The bottom of \(A\) is 1 long and the bottom of \(B\) is 3 long, so the scale factor is 3. The lines through \((2, 2)\) and \((4, 4)\), and \((3, 2)\) and \((7, 4)\), meet at \((1, 1)\). It is an enlargement, scale factor 3, centre \((1, 1)\).

    Mark scheme

    • Enlargement — B1
    • Scale factor 3 — B1
    • Centre \((1, 1)\) — B1
  4. 4 Calculate [3 marks]

    A triangle has sides of 2 cm, 3 cm and 4 cm. It is enlarged to give a similar triangle with sides of 5 cm, 7.5 cm and 10 cm. (a) Calculate the scale factor. [2 marks] (b) Calculate the perimeter of the enlarged triangle. [1 mark]

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    Model answer

    (a) \(\dfrac{5}{2} = 2.5\). (b) \(5 + 7.5 + 10 = 22.5\) cm.

    Mark scheme

    • (a) \(\dfrac{5}{2}\) or \(\dfrac{10}{4}\) — M1
    • (a) 2.5 — A1
    • (b) 22.5 cm — B1
  5. 5 Calculate [3 marks]

    The point \(A\) is \((1, 4)\). \(A\) is enlarged by a scale factor of 3 with the centre \((0, 1)\). Calculate the coordinates of the image of \(A\). [3 marks]

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    Model answer

    \(A\) is 1 right and 3 up from the centre. The image is 3 right and 9 up, at \((0 + 3, 1 + 9) = (3, 10)\).

    Mark scheme

    • Position relative to the centre, \((1, 3)\) — M1
    • \((3, 9)\) relative to the centre — M1
    • \((3, 10)\) — A1
  6. 6 Calculate [3 marks]

    The point \(A\) is \((5, 4)\). \(A\) is enlarged by a scale factor of \(-1\) with the centre \((2, 3)\). Calculate the coordinates of the image of \(A\). [3 marks]

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    Model answer

    \(A\) is 3 right and 1 up from the centre. With a scale factor of \(-1\), the image is 3 left and 1 down, at \((2 - 3, 3 - 1) = (-1, 2)\).

    Mark scheme

    • Position relative to the centre, \((3, 1)\) — M1
    • \((-3, -1)\) relative to the centre — M1
    • \((-1, 2)\) — A1

Quick check

  1. 1

    A side of 3 cm is enlarged to 12 cm. What is the scale factor?

    1. A\(9\)
    2. B\(\dfrac{1}{4}\)
    3. C\(36\)
    4. D\(4\)
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    D: \(4\)

    \(\dfrac{12}{3} = 4\).

  2. 2

    The point \((2, 3)\) is enlarged by scale factor 3 with centre \((0, 0)\). What is the image?

    1. A\((5, 6)\)
    2. B\((6, 3)\)
    3. C\((6, 9)\)
    4. D\((9, 6)\)
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    C: \((6, 9)\)

    Multiply both coordinates by 3.

  3. 3

    What happens to the angles in an enlargement?

    1. AThey are multiplied by the scale factor
    2. BThey stay the same
    3. CThey are halved
    4. DThey are added to the scale factor
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    B: They stay the same

    An enlargement keeps the angles, so the shapes are similar.

  4. 4

    What does an enlargement with scale factor \(\dfrac{1}{2}\) do to a shape?

    1. AIt halves every length
    2. BIt doubles every length
    3. CIt halves every angle
    4. DIt leaves the shape unchanged
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    A: It halves every length

    A fractional scale factor less than 1 makes the shape smaller.

  5. 5

    The centre of enlargement is \((1, 2)\) and the scale factor is 3. What is the image of \((3, 3)\)?

    1. A\((9, 9)\)
    2. B\((5, 4)\)
    3. C\((6, 5)\)
    4. D\((7, 5)\)
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    D: \((7, 5)\)

    \((3, 3)\) is 2 right and 1 up from the centre, so the image is 6 right and 3 up: \((7, 5)\).

  6. 6

    What must you give to describe an enlargement fully?

    1. AThe mirror line
    2. BThe angle and the direction
    3. CThe scale factor and the centre
    4. DA column vector
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    C: The scale factor and the centre

    An enlargement is described by its scale factor and its centre.

  7. 7

    A triangle with sides 4, 6 and 8 is enlarged to give a triangle with sides 10, 15 and 20. What is the scale factor?

    1. A\(2\)
    2. B\(2.5\)
    3. C\(6\)
    4. D\(3\)
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    B: \(2.5\)

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

  8. 8

    Which transformation is the same as an enlargement with scale factor \(-1\)?

    1. AA rotation of \(180^\circ\) about the centre
    2. BA reflection in a line through the centre
    3. CA translation
    4. DA rotation of \(90^\circ\)
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    A: A rotation of \(180^\circ\) about the centre

    Every point goes to the opposite side of the centre at the same distance.

  9. 9

    The point \((1, 3)\) is enlarged by scale factor \(-2\) with centre \((0, 0)\). What is the image?

    1. A\((2, 6)\)
    2. B\((-1, -3)\)
    3. C\((-2, 6)\)
    4. D\((-2, -6)\)
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    D: \((-2, -6)\)

    Multiply both coordinates by \(-2\).