Enlargements

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]

Mark scheme — 2 marks available

• \(7 \times 3\) — M1
• 21 cm — A1

Model answer

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

Mark scheme — 3 marks available

• 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

Model answer

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

Mark scheme — 3 marks available

• Enlargement — B1
• Scale factor 3 — B1
• Centre \((1, 1)\) — B1

Model answer

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]

Mark scheme — 3 marks available

• (a) \(\dfrac{5}{2}\) or \(\dfrac{10}{4}\) — M1
• (a) 2.5 — A1
• (b) 22.5 cm — B1

Model answer

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]

Mark scheme — 3 marks available

• Position relative to the centre, \((1, 3)\) — M1
• \((3, 9)\) relative to the centre — M1
• \((3, 10)\) — A1

Model answer

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]

Mark scheme — 3 marks available

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

Model answer

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 \(4\) Correct

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

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 \((6, 9)\) Correct
4. D \((9, 6)\)

Why: Multiply both coordinates by 3.

What happens to the angles in an enlargement?

1. A They are multiplied by the scale factor
2. B They stay the same Correct
3. C They are halved
4. D They are added to the scale factor

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

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

1. A It halves every length Correct
2. B It doubles every length
3. C It halves every angle
4. D It leaves the shape unchanged

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

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 \((7, 5)\) Correct

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

What must you give to describe an enlargement fully?

1. A The mirror line
2. B The angle and the direction
3. C The scale factor and the centre Correct
4. D A column vector

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

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 \(2.5\) Correct
3. C \(6\)
4. D \(3\)

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

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

1. A A rotation of \(180^\circ\) about the centre Correct
2. B A reflection in a line through the centre
3. C A translation
4. D A rotation of \(90^\circ\)

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

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 \((-2, -6)\) Correct

Why: Multiply both coordinates by \(-2\).