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      Describing a negative enlargement

      Lesson details

      Learning outcome

      I can describe an enlargement.

      Key learning points

      1. If the image is the opposite side of the centre of enlargement and rotated 180°, there is a negative scale factor.
      2. If the image has changed size, there has been an enlargement with scale factor ≠ 1.
      3. To describe an enlargement, you must state the centre of enlargement and the scale factor.

      Keywords

      • Transformation - A transformation is a process that may change the size, orientation or position of a shape.

      • Enlargement - Enlargement is a transformation that causes a change of size.

      • Scale factor - A scale factor is the multiplier between similar shapes that describes how large one shape is compared to the other.

      • Centre of enlargement - The centre of enlargement is the point from which a shape is enlarged.

      • Absolute value - The absolute value of a number is its distance from zero.

      Common misconception

      Pupils may want to write the transformation as two transformations, a rotation of 180° followed by an enlargement by a positive scale factor, rather than a single transformation.

      Remind pupils that a single transformation is more efficient than multiple transformations.

      Teacher tip

      Have pupils discuss how they can be sure that an enlargement by a negative scale factor has occurred rather than a rotation.

      Licence

      This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0
      except where otherwise stated. See Oak's terms & conditions
      (Collection 2).

      Lesson video

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      Prior knowledge starter quiz

      6 Questions

      Q1.
      When the scale factor of an enlargement is negative, the image is a of 180° of the object.

      Correct Answer: rotation, -ve

      Q2.
      Which diagram shows an enlargement by a positive scale factor?

      An image in a quiz
      An image in a quiz
      Correct Answer: An image in a quiz
      An image in a quiz

      Q3.
      Sam enlarges a shape. The image is smaller than the object and the orientation is different. Which of these statements is correct?

      Sam's scale factor is less than -1
      Sam's scale factor is greater than -1
      Sam's scale factor is between -1 and 1
      Sam's scale factor is between 0 and 1
      Correct answer: Sam's scale factor is between -1 and 0

      Q4.
      Shape A is enlarged by the scale factor $$-\frac{1}{3}$$ to give shape B. The scale factor that would map shape B back onto shape A is .

      Correct Answer: -3, - 3, minus 3, negative 3

      Q5.
      Shape B is enlarged to give shape A. What is the scale factor of the enlargement?

      An image in a quiz
      $$2$$
      $$\frac{1}{2}$$
      Correct answer: $$-\frac{1}{2}$$
      $$-2$$

      Q6.
      Shape A is transformed to give shape A. Describe the transformation fully.

      An image in a quiz
      An enlargement scale factor -0.5
      An enlargement scale factor -2
      Correct answer: An enlargement scale factor -3
      Correct answer: centre (3, 3)
      centre (4, 4)

      6 Questions

      Q1.
      An enlargement will produce an image that is to the object.

      Correct Answer: similar

      Q2.
      Shape A is enlarged to give shape B. Shape B is smaller than shape A. This means that the scale factor is __________.

      equal to -1
      equal to 1
      greater than -1
      less than 1
      Correct answer: between -1 and 1

      Q3.
      Which of these show an enlargement with a negative scale factor?

      An image in a quiz
      Correct Answer: An image in a quiz
      An image in a quiz
      An image in a quiz
      An image in a quiz

      Q4.
      Shape A is enlarged to give shape B. The scale factor of this enlargement is .

      An image in a quiz
      Correct Answer: -2, minus 2, negative 2, - 2

      Q5.
      Shape A is enlarged to give shape B. Describe the transformation.

      An image in a quiz
      An enlargement scale factor $$2$$, centre $$(3, 2)$$
      Correct answer: An enlargement scale factor $$\frac{1}{2}$$, centre $$(2, 3)$$
      An enlargement scale factor $$-2$$, centre $$(2, 3)$$
      An enlargement scale factor $$-\frac{1}{2}$$, centre $$(2, 3)$$
      An enlargement scale factor $$\frac{1}{2}$$, centre $$(3, 2)$$

      Q6.
      Shape A is transformed to give shape B. Describe the transformation.

      An image in a quiz
      An enlargement scale factor $$2$$, centre $$(1, 2)$$
      An enlargement scale factor $$\frac{1}{2}$$, centre $$(0, 2)$$
      An enlargement scale factor $$-2$$, centre $$(0, 2)$$
      Correct answer: An enlargement scale factor $$-2$$, centre $$(1, 2)$$
      An enlargement scale factor $$-\frac{1}{2}$$, centre $$(1, 2)$$

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