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10.5 Describing Enlargements

GCSE Maths Foundation · Edexcel · Chapter 10: Transformations

A free GCSE Maths Foundation lesson for Edexcel (9–1) from OBA School: finding the scale factor and the centre of an enlargement, and describing it fully. Watch the video, read the explanation and worked examples, then try the revision questions. You can work through the full lesson, with interactive activities, practice quizzes and printable worksheets, in our free online course.

What you will learn

  • Find the scale factor of an enlargement from matching lengths
  • Find the centre of enlargement by drawing lines through matching vertices
  • Describe an enlargement fully, including fractional scale factors
  • Use the centre and scale factor to work backwards to the object

Key words

  • Corresponding: Matching. Corresponding vertices or sides are in the same position on the object and the image.
  • Ray: A straight line drawn from a vertex of the image through the matching vertex of the object.
  • Scale factor: Image length ÷ object length.
  • Describe fully: For an enlargement: say “enlargement”, give the scale factor and give the centre.

Finding the scale factor

Choose a pair of corresponding sides. Divide the image length by the object length. Use a side you can count easily, such as a horizontal or vertical side.

Key fact: Scale factor = image length ÷ object length

  • 2 cm; Image length 6 cm; Scale factor 6 ÷ 2 = 3
  • 4 squares; Image length 10 squares; Scale factor 10 ÷ 4 = 2.5
  • 6 squares; Image length 3 squares; Scale factor 3 ÷ 6 = 1/2

Finding the centre of enlargement

Draw a straight line from each vertex of the image through the matching vertex of the object, and keep going. The lines all meet at the centre of enlargement.

Worked example: describing A → B

A has a horizontal side of 2 squares; the matching side of B is 4 squares. Scale factor = 4 ÷ 2 = 2.
The rays meet at (0, 1). Check one vertex: (3, 2) is 3 across, 1 up from (0, 1). Doubled: 6 across, 2 up gives (6, 3), which is a vertex of B.

Answer: enlargement, scale factor 2, centre (0, 1)

Fractional scale factors and going backwards

If the image is smaller than the object, the scale factor is a fraction. The centre is found in exactly the same way.

Worked example: P → Q and Q → P

P has a horizontal side of 4 squares; Q has 2 squares. Scale factor = 2 ÷ 4 = 1/2. The rays meet at (1, 1).
P → Q: enlargement, scale factor 1/2, centre (1, 1).
Q → P goes the other way: enlargement, scale factor 2, same centre (1, 1).

Answer: scale factor 1/2 one way, 2 the other way

Key fact: To go back from the image to the object, use the reciprocal scale factor (turn the fraction upside down) and the same centre.

Common mistakes

  • Dividing the wrong way round: scale factor = image ÷ object, not object ÷ image.
  • Giving only part of the description. You need the word enlargement, the scale factor and the centre.
  • Joining non-matching vertices, so the rays do not meet at a single point.
  • Writing a fractional scale factor as a negative number. A smaller image has a scale factor between 0 and 1.

Revision questions

Try these, then check your answers below each one.

Question 1. In an enlargement, a side of 4 cm becomes 14 cm. Work out the scale factor.

Answer: 3.5

Working: 14 ÷ 4 = 3.5.

Question 2. In an enlargement, a side of 12 cm becomes 3 cm. Work out the scale factor as a decimal.

Answer: 0.25

Working: 3 ÷ 12 = 0.25 (which is 1/4).

Question 3. How do you find the centre of an enlargement on a grid? (Choose from: Draw lines through matching vertices of the image and object; they meet at the centre, Find the midpoint of the two shapes, Measure the angle between the shapes, Find the point halfway between two vertices of the image.)

Answer: Draw lines through matching vertices of the image and object; they meet at the centre

Working: Lines (rays) through each pair of matching vertices all pass through the centre of enlargement.

Related lessons

Continue in the full course

This lesson is section 10.5 (EGCMF1005) of our free GCSE Maths Foundation course. In the full course you get every video for this section, an animated interactive lesson, a self-marking practice quiz, a printable worksheet with a mark scheme, and your progress saved. Go to the full GCSE Maths Foundation course.

 

 

 

 

 

 

 

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