# Enlargement (Fractional Scale Factor)

In this worksheet, students practise enlarging a shape from a given point with a fractional scale factor.

Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   AQA, Pearson Edexcel, Eduqas, OCR

Curriculum topic:   Geometry and Measures, Basic Geometry

Curriculum subtopic:   Properties and Constructions, Conventions, Notations and Terms

Difficulty level:

### QUESTION 1 of 10

Normally, when you are enlarging an object in GCSE Maths, you have to be able to enlarge from a given point.

Previously, we discussed how to enlarge from a point. Today, we will be looking at fractional scale factors.

What does a fractional scale factor do?

Scale factors that are larger than 1 will make a shape larger

Scale factors between 0 and 1 will make an object smaller.

Example 1: Enlarge the shape by a scale factor of 1/2 about the point (2,1)

Step 1: Draw the centre of enlargement on the grid.

Doing this means you wont forget where you're enlarging from.

Step 2: Find the movement from the centre to one of the points on the shape.

We can see that to get to the bottom left corner, we move 2 right and 4 up

Step 3: Multiply this movement by the Scale Factor.

Our scale factor is 1/2, so this movement halves to 1 right and 2 up.

Step 4: Plot this point on the diagram.

When you are plotting this point, it is vital that you count from the centre of enlargement.

Step 5: Repeat steps 2 - 4 for the other corners of the shape.

Step 6: Draw the enlarged shape and label the image and enlargement.

Example 2: Shape A is enlarged to shape A'. Find the scale factor and centre of enlargement.

Finding the Scale Factor.

All we have to do here is to look at one of the pairs of sides. If we use the bottom of each shape, shape A is 3cm long and shape A' is 1 cm long.

This gives a scale factor of 1/3.

Finding the centre of enlargement.

To find this, we join up two pairs of matching corners with striaght lines and see where they join up.

We can see here that the two lines join up at the point (1,0). This is the centre of enlargement.

A fractional scale factor will normally make an object...

Rectangle ABCD is enlarged by SF 1/2 around the point (0,0).

Find the coordinates of a'

Rectangle ABCD is enlarged by SF 1/2 around the point (0,0).

Find the coordinates of d'

Rectangle ABCD is enlarged by SF 1/3 around the point (2,1).

Find the coordinates of b'

Rectangle ABCD is enlarged by SF 1/3 around the point (2,1).

Find the coordinates of c'

Shape a is enlarged around the point (0,0). What is the SF of the enlargement?

Shape a is enlarged to shape a'. Find the SF and centre of the enlargement.

A fractional SF will make a shape smaller.

Always true

Sometimes true

Never true

The triangle abc is enlarged with a SF of  1/2 about the point (2,2).

What are the coordinates of a',b' and c'

 Coordinate a' b' c'

The rectangle abcd is enlarged with a SF of  3 about the point (1,-1).

What are the coordinates of a',b',c' and d'

 Coordinate a' b' c' d'
• Question 1

A fractional scale factor will normally make an object...

EDDIE SAYS
Any fraction between 0 and 1 will make an object smaller. You need to be careful with fractions larger than 1 (i.e. 4/3) as these will make the object larger.
• Question 2

Rectangle ABCD is enlarged by SF 1/2 around the point (0,0).

Find the coordinates of a'

(2,2)
EDDIE SAYS
To get from the centre (0,0) to point A is a movement of 4 right and 4 up. If we halve this (SF 1/2), we get a movement of 2 right and 2 up. We then do this movement from the centre to get the point a'.
• Question 3

Rectangle ABCD is enlarged by SF 1/2 around the point (0,0).

Find the coordinates of d'

(2,3)
EDDIE SAYS
To get from the centre (0,0) to point D is a movement of 4 right and 6 up. If we halve this (SF 1/2), we get a movement of 2 right and 3 up. We then do this movement from the centre to get the point d'.
• Question 4

Rectangle ABCD is enlarged by SF 1/3 around the point (2,1).

Find the coordinates of b'

(6,3)
EDDIE SAYS
To get from the centre (2,1) to point B is a movement of 9 right and 6 up. If we divide by 3 (SF 1/3), we get a movement of 3 right and 2 up. We then do this movement from the centre to get the point b'.
• Question 5

Rectangle ABCD is enlarged by SF 1/3 around the point (2,1).

Find the coordinates of c'

(10,9)
EDDIE SAYS
To get from the centre (2,1) to point C is a movement of 9 right and 9 up. If we divide by 3 (SF 1/3), we get a movement of 3 right and 3 up. We then do this movement from the centre to get the point c'.
• Question 6

Shape a is enlarged around the point (0,0). What is the SF of the enlargement?

1/2
0.5
EDDIE SAYS
If we count the length of the sides in a and a', we see that a' is half the length of a.
• Question 7

Shape a is enlarged to shape a'. Find the SF and centre of the enlargement.

EDDIE SAYS
Comparing the sides shows that a' is one third of the length of a Drawing lines back through the corners will give the centre of enlargement.
• Question 8

A fractional SF will make a shape smaller.

Sometimes true
EDDIE SAYS
Most of the time it will make the object smaller. This happens if the scale factor is between 0 and 1 If the scale factor is a fraction greater than 1 (3/2, 11/3 etc) it will make the object larger.
• Question 9

The triangle abc is enlarged with a SF of  1/2 about the point (2,2).

What are the coordinates of a',b' and c'

 Coordinate a' b' c'
EDDIE SAYS
Does it matter that the centre of enlargement is in the middle of the shape? Not at all, we do it in the same way. For example, to get the coordinate of c'. We find the movement from our centre (2,2) to point C - This is 2 square up Halving this (SF1/2) gives a movement of 1 up from the centre. This gives the coordinate of c' as (2,3)
• Question 10

The rectangle abcd is enlarged with a SF of  3 about the point (1,-1).

What are the coordinates of a',b',c' and d'

 Coordinate a' b' c' d'
EDDIE SAYS
Does it matter that the centre is over the x - axis? Not at all, we do it in the same way. For example, to get the coordinate of a'. We find the movement from our centre (0,3) to the point a - This is 6 squares up Dividing this by 3 (SF1/3) gives a movement of 2 squares up from the centre This gives the coordinate of a' as (1,1)
---- OR ----

Sign up for a £1 trial so you can track and measure your child's progress on this activity.

### What is EdPlace?

We're your National Curriculum aligned online education content provider helping each child succeed in English, maths and science from year 1 to GCSE. With an EdPlace account you’ll be able to track and measure progress, helping each child achieve their best. We build confidence and attainment by personalising each child’s learning at a level that suits them.

Get started