Identify dilations Identify scale factors and use scale factors to solve problems Write and simplify ratios Use proportions to solve problems

1. Dilation, Scale Factor, & Proportion
The student is able to (I can):
• Identify dilations
• Identify scale factors and use scale factors to solve
problems
• Write and simplify ratios
• Use proportions to solve problems

2. Reminder:Reminder:Reminder:Reminder:
transformationtransformationtransformationtransformation – a change in the position, size, or shape of a
figure.
preimagepreimagepreimagepreimage – the original figure.
imageimageimageimage – the figure after the transformation.
A
B C
A´´´´
B´´´´ C´´´´

3. dilationdilationdilationdilation – a transformation that changes the size of a figure
but not the shape.
Example:
Tell whether each transformation appears to be a dilation.
1. 2.
SS
yes no

4. ratioratioratioratio – a comparison of two numbers by division.
The ratio of two numbers a and b, where b does not equal 0
(b ≠ 0) can be written as
a to b
a : b
Example: The ratio comparing 1 and 2 can be written 1 to 2,
1 : 2, or .
To compare more than two numbers, use “dot”
notation. Ex. 3 : 7 : 9
a
b
1
2

5. proportionproportionproportionproportion – an equation stating that two ratios are equal.
Two sets of numbers are proportionalproportionalproportionalproportional if they use the same
ratio.
Example: or a : b = c : d
Cross Products Property
In a proportion, if , and b and d ≠ 0, then ad = bc
=
a c
b d
a c
b d
=

6. scalescalescalescale factorfactorfactorfactor – the ratio of the image to the preimage.
If k < 1, the figure gets smaller; if k > 1, the figure gets larger.
•
•
•
X´´´´
Y´´´´
Z´´´´
•
•
•
P
X
Y
Z
center of
dilation
X Y Y Z X Z
k
XY YZ XZ
′ ′ ′ ′ ′ ′
= = =

7. Examples
1. What is the scale factor of the dilation?
2. If you are enlarging a 4x6 photo by a scale factor of 4,
what are the new dimensions?
10
24
5
12

8. Examples
1. What is the scale factor of the dilation?
2. If you are enlarging a 4x6 photo by a scale factor of 4,
what are the new dimensions?
4(4) = 16 6(4) = 24
New dimensions = 16x24
10
24
5
12
5 1 12 1
(or )
10 2 24 2
k k= = = =

9. Examples Solve each proportion:
1.
2.
3.
3
8 32
x
=
4 2
5x
=
2
6 3
x x −
=

10. Examples Solve each proportion:
1.
8x = 96 x = 12
2.
2x = 20 x = 10
3.
3x = 6(x – 2)
3x = 6x – 12
–3x = –12 x = 4
3
8 32
x
=
4 2
5x
=
2
6 3
x x −
=

11. Examples 4. The ratio of the angles of a triangle is
2: 2: 5. What is the measure of each
angle?

12. Examples 4. The ratio of the angles of a triangle is
2: 2: 5. What is the measure of each
angle?
2x + 2x + 5x = 180˚
9x = 180˚
x = 20
2(20) = 40˚
2(20) = 40˚
5(20) = 100˚