8.3 Scale Diagrams
A __________ ___________________ is a reproduction of a diagram. It is either larger or
smaller than the original, but it has the same shape (ie. It is ___________.) Each dimension of
the figure is multiplied by the same __________ ___________________.
In order to visualize the actual figure, you need to know the scale of the scale drawing. You will
need to use ratios and convert measurement units.
The scale of a diagram can be specified in four ways:
1. As a statement. (1 cm = 50 km)
 1cm 

 50km 
2. As a rate. 
3. As a ratio. (1 : 5 000 000).
4. As a linear scale.
50
100
150
200
250
If the image length is larger than the object length, then the
scale factor is greater than 1 and we have an enlargement.
If the image length is less than the object length, then the scale factor is less than 1 and we have a reduction.
The equation:
Example 1:
represents the calculation of scale factor (k).
Complete the table:
Object Length
Image Length
7 cm
14 cm
15 in
5 in
6m
8 ft
Scale Factor
1.5
0.4
Enlargement or
Reduction
Example 2:
a.
Surveyors are using a measuring device called a tight-chain to determine
boundaries of plots of land. Two surveyors determine that a proposed building
site is rectangular, measuring 175 m by 50 m. To make a scale drawing of the
site, they use a scale of 1 : 2500.
What are the dimensions of the scale drawing of the building site in centimetres?
1
of the actual size of a house. If a chair in the dollhouse is
10
2.75 cm tall, how tall is the actual chair that it models?
Example 3:
A dollhouse is
Example 4:
A portrait measures 50 cm by 35 cm. The larger side of a reduction of it measures
20 cm.
a.
What is the scale factor of the reduction?
b.
What is the length of the shorter side of the reduction?