- Identify dilations and scale factors and use them to solve problems - Write and simplify ratios and use proportions to solve problems - Key concepts covered include: dilations, scale factors, ratios, proportions, and using them to solve problems involving transformations and ratios of quantities

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. transformation
preimage
image
A change in the position, size, or shape of
a figure.
The original figure.
The figure after the transformation.
A
B C
A´
B´ C´

3. dilation 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. ratio A comparison of two numbers by division.
The ratioratioratioratio 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 .
Note: To compare more than two numbers,
use “dot” notation. Ex. 3 : 7 : 9
a
b
1
2

5. ratio
proportion
A comparison of two or more numbers.
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. scale factor 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. Example 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
k (or k )
10 2 24 2
= = = =

8. 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 x
8 32
=
4 2
x 5
=
x x 2
6 3
−
=

9. 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˚