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Objectives:C Grade Enlarge a shape by a fractional scale factor

Compare the area of an enlarged shape with the original shapeFind the centre of enlargement

B Grade Distinguish between formulae for perimeter, area and volume by considering dimensions

A Grade Compare areas and volumes of enlarged shapesEnlarge a shape by a negative scale factor

Prior knowledge:

Enlarge an object by a positive integer scale factorusing a centre of enlargement and ray lines.

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Enlargement is not just for making an object bigger using the scale factor

Objects can be enlarged using any number as a scale factor including fractions and negative numbers.

object

CoE

Using a scale factor ½ the distance from the CoE to the image vertices is ½ times the distance from the CoE to the object vertices.

Scale Factor ½Distance from CoE2 squares right 1 square down

4 squares right 2 squares down

xScale Factor ½Distance from CoE5 squares right 1 square down

10 squares right 2 squares down

x

Scale Factor ½Distance from CoE2 squares right 3 squares down

4 squares right 6 squares down

x

This gives us enough information to draw the image

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Negative scale factors can also be used

-8 -7 -6 -5 -4 -3 -2 - 1 0 1 2 3 4 5 6 7 8 9

5

4

3

2

1

-1

- 2

- 3

- 4

- 5

CoE

A negative scale factor takes the image the opposite side of the centre of enlargementEnlarge the object by a scale factor of -2

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-8 -7 -6 -5 -4 -3 -2 - 1 0 1 2 3 4 5 6 7 8 9

5

4

3

2

1

-1

- 2

- 3

- 4

- 5

CoE

Enlarge the object by a scale factor of -3

Notice how the image is upside down from the object

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In each case object A has been enlarged to image BFind the scale factor and centre of enlargement for

A A

B

B

AB

A

B

Scale Factor ½

Scale Factor -1

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In each case object A has been enlarged to image BFind the scale factor and centre of enlargement for

A A

B

B

A B

A

B

Worksheet 3