Syllabus Edition

First teaching 2021

Last exams 2024

Enlargements (CIE IGCSE Maths: Core)

Revision Note

Test Yourself

Author

Paul

Expertise

Maths

Enlargements

What is an enlargement?

An enlargement is a transformation that changes the size of the shape
- The scale factor tells you how many times bigger each edge of the enlarged image will be compared to the corresponding edge on the original object
- If the scale factor is greater than 1, the enlarged image will be bigger than the original object
- If the scale factor is less than 1, the enlarged image will be smaller than the original object
  - See Fractional Enlargements
The position of a shape will also change with enlargement
- This is determined by the centre of enlargement (CoE)
- The centre of enlargement is a coordinate point on the grid
The orientation of the shape will be the same for a positive enlargement
- We do not need to consider negative enlargements for this course

How do I enlarge a shape?

You need to be able to perform an enlargement (on a coordinate grid)
STEP 1
Starting from the centre of enlargement, count the horizontal and vertical distances to any one vertex on the original shape
STEP 2
Multiply both the horizontal and vertical distances by the given scale factor
STEP 3
Starting again from the centre of enlargement, and counting in the same directions
- measure these new (multiplied) horizontal and vertical distances
- mark the position on the grid of the corresponding vertex on the enlarged image
STEP 4
Repeat Steps 1 to 3 for the remaining vertices
- You may not need to do this for every vertex, if you are confident you can draw the enlarged shape once a couple of vertices are in place
- We'd recommend you do at least two vertices though to be sure
STEP 5
Connect the vertices on the enlarged image and label it

How do I describe an enlargement?

You need to be able to identify and describe an enlargement when presented with one
You must fully describe a transformation to get full marks
For an enlargement, you must:
- State that the transformation is an enlargement
- State the scale factor
- Give the coordinates of the centre of enlargement

Exam Tip

Make sure that you always start from the centre of enlargement
- this is both for measuring distances to the original object and then measuring for the enlarged image
- a common mistake is to measure the distance between a pair of corresponding vertices on the original object and enlarged image
You can check your work by drawing straight lines through the centre of enlargement and a pair of corresponding vertices on the original object and the enlarged image
- All such lines should intersect at the centre of enlargement

Worked example

On the grid below enlarge shape C using scale factor 2 and centre of enlargement (2, 1).

Label your enlarged shape C'.

Enlargement-Q1, IGCSE & GCSE Maths revision notes

Start by marking on the centre of enlargement (CoE).
Count the number of squares in both a horizontal and vertical direction to go from the CoE to one of the vertices on the original object, this is 2 to the right and 3 up in this example.
As the scale factor is 2, multiply these distances by 2, so they become 4 to the right and 6 up.
Count these new distances from the CoE to the corresponding point on the enlarged image and mark it on.
Draw a line through the CoE and the pair of corresponding points, they should line up in a straight line.

Enlargement-Q1-working, IGCSE & GCSE Maths revision notes

Repeat this process for each of the vertices on the original object (or at least 2).
Join adjacent vertices on the enlarged image as you go.
Label the enlarged image C'.

Enlargement-Q1-Final-Answer, IGCSE & GCSE Maths revision notes

Describe fully the single transformation that creates shape B from shape A.

Enlargement-Q2, IGCSE & GCSE Maths revision notes

We can see that the image is larger than the original object, therefore it must be an enlargement.
As the enlarged image is bigger than the original object, the scale factor must be greater than 1.
Compare two corresponding edges on the object and the image to find the scale factor.

The height of the original "H" is 3 squares
The height of the enlarged "H" is 9 squares

$∴ Scale Factor = \frac{9}{3} = 3$

Draw a straight line through the CoE and a pair of corresponding points on the original object and the enlarged image.
Repeat this step for as many vertices as you feel you need to so you can confidently locate the CoE.
Do this for all pairs of vertices to be sure!
The point of intersection of the lines is the CoE.

Enlargement-Q2-Working, IGCSE & GCSE Maths revision notes

Shape A has been enlarged using a scale factor of 3 and a centre of enlargement (9, 9) to create shape B

Fractional Enlargements

What is meant by fractional enlargements?

This is where the scale factor is less than 1
- i.e. the scale factor is a fraction

How do I enlarge a shape with a fractional scale factor?

The process is no different as to when we are dealing with a positive scale factor
- Measure the horizontal and vertical distances from the centre of enlargement (CoE) to any one vertex
- Multiply these distances by the scale factor
  - This is where things will different as the 'new' distances will be smaller than the 'original' distances
- Measure the new distances from the centre of enlargement to find the position of the new vertex
- Repeat for all vertices or as many as you need to fill confident of being able to complete the enlargement
The big difference is in the visual result - the 'enlarged' shape will be smaller and closer to the centre of enlargement than the original
- Mathematically though, these are still 'called enlargements'

How do I describe an enlargement with a fractional scale factor?

You need to be able to identify when a fractional scale factor has been using in an enlargement
- Look for the enlarged shape being smaller than the original
To gain full marks you will still need to
- state that the transformation is an enlargement
- state the scale factor (as a fraction)
- give the coordinates of the centre of enlargement

Exam Tip

Still ensure you measure from the CoE when measuring distances to both the original shape and enlarged shape
Then check using lines through corresponding vertices, intersecting at the CoE still applies
- However this can get confusing and untidy on small diagrams

Worked example

\begin{matrix}  \end{matrix}

On the grid below enlarge shape C using scale factor

\frac{1}{2}

and centre of enlargement (4, 2).

Write down the four vertices of your enlarged shape. $cie-igcse-core-fractional-enlargements-rn-we-a1-image$

Mark the centre of enlargement at (4, 2)
Count the number of squares horizontally and vertically to any vertex - we've chosen the vertex at (-2, 4)

$cie-igcse-core-fractional-enlargements-rn-we-a2-image$

Multiply these distance by the scale factor, $\frac{1}{2}$

6 'right

\times \frac{1}{2} = 3

'right'

2 'down' $\times \frac{1}{2} = 1$ 'down'

Count these new distances (which should be smaller than the originals) from the CoE to find the corresponding point on the new image and mark it on

Repeat as required and draw lines through corresponding vertices and the CoE as a check

$cie-igcse-core-fractional-enlargements-rn-we-a3-image$

The four vertices of the enlarged shape are (0, 0), (0, 4), (1, 3) and (1, 1)

Use a logical order, working your way round the shape slowly, to ensure you do miss any vertices out.

Describe fully the single transformation that creates shape B from shape A.

$cie-igcse-core-fractional-enlargements-rn-we-b1-image$

We can see the image is smaller than the original so it is a fractional enlargement
Compare two corresponding edges to find the scale factor - we've used the top edge

scale factor = $\frac{new edge}{old edge} = \frac{2}{6} = \frac{1}{3}$

Draw straight lines through corresponding vertices on the original shape
Repeat this 3-4 times and you should find the lines intersect at the same point
This point will be the CoE

$cie-igcse-core-fractional-enlargements-rn-we-b2-image$

Shape A has been enlarged using a scale factor of $\frac{1}{3}$ and a centre of enlargement (3, -3.5) to create shape B

You've read 0 of your 0 free revision notes

Get unlimited access

to absolutely everything:

Downloadable PDFs
Unlimited Revision Notes
Topic Questions
Past Papers
Model Answers
Videos (Maths and Science)

Join the 100,000+ Students that ❤️ Save My Exams

the (exam) results speak for themselves:

Test yourself Next topic

Did this page help you?