Finding the centre of enlargement

Finding the centre of enlargement

Pencil and paper
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Working with Students
Further Resources
This task is about the centre of enlargement and enlarging by a scale factor.

 

The bigger triangle PQR has been "enlarged" to become the smaller triangle P' Q' R' .

 
a)
On the diagram above draw the centre of enlargement and label it C.
Leave in your construction marks.
 
b) What is the scale factor for the enlargement? __________
Task administration: 
This task can be completed with pencil and paper.
Level:
5
Curriculum info: 
Maths, Geometry and Measurement, Transformation
Keywords: 
enlargement, resizing, centre of enlargement, scale factor
Description of task: 
Students identify the centre of enlargement and the scale factor for an enlargement on a grid.
Learning Progression Frameworks
This resource can provide evidence of learning associated with
Geometric thinking, set 6
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 

 

Y11 (03/2000)

a)

The point (⁻1, ⁻2) is labelled C.
At least two construction lines join points P and P', Q and Q' and R and R'.

very difficult
difficult

b)

 1/3 [Accept 0.333]

difficult
Diagnostic and formative information: 
 

Common error

Likely calculation

Likely reason

a)

(3,2)

  

Centroid of PQR.

b)

3

( 1⁄3 )-1

Gives scale factor for enlargement of P' Q' R' → PQR rather than vice versa.

9 (or 1⁄9 )

32

Gives increase in area when enlarging P' Q' R' → PQR.