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EnlargementsIf a shape (object) is enlarged in such a way, that all lengths become twice the size they were on the original then we say that the shape has been enlarged by a SCALE FACTOR of x2.

A

BObject

Objectx2

x2

3

2A’

Image

6

4

4

3B’

Image

8

6

We say that the rectangle A has been enlarged by a scale factor of x2 to become image A’. Similarly B’ is the image of triangle B after a x2 enlargement.

EnlargementsIn a similar manner, if a shape (object) is enlarged in such a way, that all lengths become three times the size they were on the original then we say that the shape has been enlarged by a SCALE FACTOR of x3.

Object

x3

A’

Image

A2

5

4

6

15

12

Enlargements

Question 1. Object A is to be enlarged by a scale factor of enlargement of x2 and object B by a scale factor of enlargement of x 3. Draw and label the images. The points are there to help you with the positioning of the images.

B

Object

A

Object

B’

Image

A’

Image

Enlargements

Question 2. Only one of the triangles shown is an enlargement of triangle A. Which triangle is it and what is the scale factor of enlargement?

A

BCD

E

Triangle D, scale factor of enlargement is x 2

Enlargements

Question 3. Two of the trapezia shown are enlargements of trapezium A. Which trapezia are they and what are the scale factors of enlargement?E is an enlargement by scale factor x2 and C is an enlargement by scale factor x 3

A

B

D

C

E

F

Fractional

EnlargementsFractional Scale FactorsIf a shape (object) is enlarged in such a way, that all lengths become ½ the size they were on the original then we say that the shape has been enlarged by a SCALE FACTOR of x½.

B’Image

A’

Image

x½

A

Object

B

Object

3

2

6

4

4

3

8

6

x½

EnlargementsIn a similar manner, if a shape (object) is enlarged in such a way, that all lengths become 1/3 the size they were on the original then we say that the shape has been enlarged by a SCALE FACTOR x1/3.

x1/3

A

Object

Image

A’2

5

4

6

15

12

EnlargementsQuestion 4. (a) Enlarge the rectangle by a scale factor of enlargement of x¼ (b) Enlarge the triangle by a scale factor of enlargement of x 1/3. (c) Enlarge the kite by a scale factor of enlargement of x 1/2.

Object

B’

Image

Object

AB

Object

A’

Image

C

C’

Image

Enlargements

Question 5. Only one of the triangles shown is an enlargement of triangle D. Which triangle is it and what is the scale factor of enlargement?

A

BC

D

E

Triangle A, scale factor of enlargement is x½

EnlargementsQuestion 6. Some of the trapezia shown are enlargements of C. Which ones are they and what is the scale factor of enlargement in each case?

A is an enlargement of C by scale factor x 1/3.

A

B

D

C

E

F

D is an enlargement of C by scale factor x ½. E is an enlargement of C by scale factor x 2/3.

Areas and Volumes

EnlargementsAreas and Volumes (Extension)

4

3 Area = 12

Investigate what happens to the area of the rectangle shown when it is enlarged by scale factors of enlargement of x2, x3, x4, and x5. Tabulate your results and make a statement.

SF x1 x2 x3 x4 x5

Dimensions

3 x 4 6 x 8 9 x 12 12 x 16 15 x 20

Area units2

12 48 108 192 300

= 12 x 12 = 12 x 22 = 12 x 32 = 12 x 42 = 12 x 52

The area factor is the square of the scale factor of enlargement.

Enlargements

3

2

Investigate what happens to the volume of the cuboid shown when it is enlarged by scale factors of enlargement of x2, x3, x4, and x5. Tabulate your results and make a statement.

Volume x1 x2 x3 x4 x5

Dimensions

1 x 2 x 3 2 x 4 x 6 3 x 6 x 9 4 x 8 x 12 5 x 10 x 15

Vol units3 6 48 162 384 750

= 6 x 13 = 6 x 23 = 6 x 33 = 6 x 43 = 6 x 53

The volume factor is the cube of the scale factor of enlargement.

1

Areas and Volumes (Extension)

Enlargements

Question 1. Object A is to be enlarged by a scale factor of enlargement of x2 and object B by a scale factor of enlargement of x 3. Draw and label the images. The points are there to help you with the positioning of the images.

B

Object

A

Object

Worksheets

EnlargementsQuestion 3. (a) Enlarge the rectangle by a scale factor of enlargement of x¼ (b) Enlarge the triangle by a scale factor of enlargement of x 1/3. (c) Enlarge the kite by a scale factor of enlargement of x 1/2.

Object

Object

AB

Object

C