OpenRevise

Exam questions · Maths · Transformations and Similarity

Enlargements

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

    A rectangle is 3 cm by 5 cm. It is enlarged by a scale factor of 4. Write down the length and the width of the enlarged rectangle.

    Show answerHide answer

    Model answer

    Each length is multiplied by 4, so the enlarged rectangle is \(3 \times 4 = 12\) cm by \(5 \times 4 = 20\) cm.

    Mark scheme

    • \(3 \times 4\) or \(5 \times 4\) — M1
    • 12 cm by 20 cm — A1
  2. 2 Enlarge [3 marks]

    Enlarge triangle \(T\) by a scale factor of 3 with the centre of enlargement \(O\), the origin. (3 marks)

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

    Model answer

    Multiply each coordinate by 3: \((1, 1)\) goes to \((3, 3)\), \((3, 1)\) goes to \((9, 3)\) and \((1, 2)\) goes to \((3, 6)\).

    Mark scheme

    • Enlarges at least two vertices by a scale factor of 3 — M1
    • At least two vertices correct — A1
    • Triangle with vertices \((3, 3)\), \((9, 3)\) and \((3, 6)\) — A1
  3. 3 Describe [3 marks]

    Describe fully the single transformation that maps triangle \(A\) onto triangle \(B\).

    Triangle A and its image triangle B on a grid.
    Show answerHide answer

    Model answer

    The bottom of \(A\) is 2 long and the bottom of \(B\) is 4 long, so the scale factor is 2. The lines through matching corners, such as \((2, 1)\) and \((3, 2)\), and \((4, 1)\) and \((7, 2)\), meet at \((1, 0)\). So it is an enlargement, scale factor 2, centre \((1, 0)\).

    Mark scheme

    • Enlargement — B1
    • Scale factor 2 — B1
    • Centre \((1, 0)\) — B1
  4. 4 Work out [3 marks]

    A triangle has sides of 4 cm, 6 cm and 8 cm. It is enlarged by a scale factor of 1.5. (a) Work out the lengths of the sides of the enlarged triangle. (2 marks) (b) Work out the perimeter of the enlarged triangle. (1 mark)

    Show answerHide answer

    Model answer

    (a) \(4 \times 1.5 = 6\), \(6 \times 1.5 = 9\) and \(8 \times 1.5 = 12\). (b) \(6 + 9 + 12 = 27\) cm.

    Mark scheme

    • (a) At least one length multiplied by 1.5 — M1
    • (a) 6 cm, 9 cm and 12 cm — A1
    • (b) 27 cm — B1 (follow through from (a))
  5. 5 Work out [3 marks]

    A square has sides of 12 cm. It is enlarged by a scale factor of \(\dfrac{1}{3}\). (a) Write down the side length of the enlarged square. (1 mark) (b) Work out the area of the enlarged square. (2 marks)

    Show answerHide answer

    Model answer

    (a) \(12 \times \dfrac{1}{3} = 4\) cm. (b) \(4 \times 4 = 16\) cm\(^2\).

    Mark scheme

    • (a) 4 cm — B1
    • (b) \(4 \times 4\) — M1
    • (b) 16 cm\(^2\) — A1 (follow through from (a))
  6. 6 Work out [3 marks]

    The point \(A\) is \((3, 2)\). \(A\) is enlarged by a scale factor of \(-2\) with the centre \((1, 1)\). Work out the coordinates of the image of \(A\).

    Show answerHide answer

    Model answer

    \(A\) is 2 right and 1 up from the centre. With a scale factor of \(-2\), the image is 4 left and 2 down from the centre, at \((1 - 4, 1 - 2) = (-3, -1)\).

    Mark scheme

    • Position relative to the centre, \((2, 1)\) — M1
    • \((-4, -2)\) relative to the centre — M1
    • \((-3, -1)\) — 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\(4\)
    Show answerHide answer

    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\((9, 6)\)
    Show answerHide answer

    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
    Show answerHide answer

    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
    Show answerHide answer

    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\((7, 5)\)
    Show answerHide answer

    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
    Show answerHide answer

    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\(3\)
    Show answerHide answer

    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 \(90^\circ\)
    Show answerHide answer

    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\((-2, -6)\)
    Show answerHide answer

    D: \((-2, -6)\)

    Multiply both coordinates by \(-2\).