Scale Factor

Scale factor = new measurement old measurement

- Scale factor more than 1 => shape gets bigger

(Enlargement)- Scale factor less than 1 => shape gets smaller (Reduction)- Congruent shapes are similar shapes with SF = 1

Old measurement x Scale factor = new measurement

Reductions, Reductions, Enlargements and the Enlargements and the

Scale FactorScale Factor

4

3

A

B C

Triangle ABC needs to be enlarged by a scale factor of 3.

What do we need to do first?

What do we need to do second?

5

4

3

A

B C

What do you notice about the new drawing? What about its ‘name’?

The new triangle is called ________ with side lengths:A’B’ = _______B’C’ = _______A’C’ = _______

5

4

8

9

J

K L

Triangle JKL needs to be reduced by a scale factor of 0.5.

What are the new side lengths of triangle J’K’L’?

4

8

9

J

K L

J’K’ = 4 x ________K’L’ = 8 x ________J’L’ = 9 x _________

So Triangle J’K’L’ now looks like this:

Determining Scale Determining Scale FactorFactor

BC

A

G

H

I2 cm

8 cm

5 cm 20 cm

6 cm

24 cm

These two triangles are similar because the ratio of corresponding sides is the same.

The scale factor from the small triangle to the larger triangle is 4!

x 4

x 4

x 4

To find the scale factor can you determine what factor was multiplied by a side length to create the corresponding side length?

The scale of the drawing can be written as 1cm : 4 cm

Determining Scale Determining Scale FactorFactor

W

H B

R

V M

10 ft8 ft

6 ft

20 ft

16 ft

12 ft

What was the scale factor used to create the smaller triangle?

What type of factor creates a smaller product?

x ½

x ½

x ½

The scale factor used is ½ or 0.5.

The scale of the drawing can be written as 2 feet:1 foot

Using Scale Factor to Solve for Using Scale Factor to Solve for

Missing Side LengthsMissing Side LengthsSolve for the missing side GH.T

U

V

F

G

H

10 ft

15 ft

20 ft

4 ft

3 ft

Determine the scale factor…1

5

1

5

1

5

1

5

Now multiply the scale factor by the original side… 110

52 ft

If you cannot determine the scale factor divide:dilated side

corresponding original side

The scale of the drawing is: 5 feet :1 feet

If two objects are similar then one is an enlargement of the other

The rectangles below are similar:

Find the scale factor of enlargement that maps A to B

A

B

8 cm

16 cm5 cm

10 cm

Not to scale!

Scale factor = x2

Note that B to A

would be x ½

If two objects are similar then one is an enlargement of the other

The rectangles below are similar:

Find the scale factor of enlargement that maps A to B

A

B

8 cm

12 cm5 cm

7½ cm

Not to scale!

Scale factor = x1½

Note that B to A

would be x 2/3

8 cm

If we are told that two objects are similar and we can find the scale factor of enlargement then we can calculate the value of an unknown side.

AB

3 cm

Not to scale!

24 cm

x cm

Comparing corresponding sides in A and B: 24/8 = 3 so x = 3 x 3 = 9 cm

5.6 cm

If we are told that two objects are similar and we can find the scale factor of enlargement then we can calculate the value of an unknown side.

AB

2.1 cm

Not to scale!

x cm

7.14 cm

Comparing corresponding sides in A and B: 7.14/2.1 = 3.4 so x = 3.4 x 5.6 = 19.04 cm

Given the shapes are similar, find the values y and z ?

Scale Factor applies to ANY SHAPES that are mathematically similar.

15 cm

3 cm

7 cm

2cm

yz

6 cm

Scale factor = ESF = 3

15= 5

is 2 x 5 = 10

1.4 cm

Scale factor = RSF = 5

1

is 6 x 0.2 = 1.2

= 0.2

y z

Scale factors Scale factors

8cm12cm

Enlargement Scale factor?

Reduction Scale factor?

5cm

7.5cm

ESF =

RSF =

Can you see the relationship between the two scale factors?w

ww

.mat

hsre

visi

on.c

om

12

8812

3

2=

2

3=

9cm a

Find a given ESF = 3

b

15cm

By finding the RSF Find the value of b.

ESF = 3 a9

=

Scale factors Scale factors w

ww

.mat

hsre

visi

on.c

om

27cm

5cm

1

3RSF =

b

15= =

5

15