Scale Factor

All scale drawings must have a scale written on
them. Scales are usually expressed as ratios.
Normally for maps and buildings the ratio:
Drawing length: Actual length
For maps the ratio is normally in the ratio:
Map distance: Actual Distance
Example: 1cm : 100cm
The ratio 1cm:100cm means that for every 1cm on the scale
drawing the length will be 100cm in real life
Example: 1:10000
The ratio 1:10000 means that the real distance is 10000
times the length of one unit on the map or drawing.
 When a figure is dilated, its size is changed by multiplying the length of
each side by a scale factor. All angles remain the same and so the
new shape (or image) is similar to the original.
 Can be found by dividing a new side length by the original side length.
When going from a small shape to a larger shape the scale factor is
greater than 1. (Enlargement)

•When going from a large shape to a smaller shape the scale factor is
•less than 1. (Reduction)

Determine the corresponding side lengths.
Determine if you are making a larger shape or a smaller shape.
Determine if the scale factor is greater than or less than 1.
Write the correct ratio.
Scale factor = new measurement
old measurement
Old measurement x SF = new measurement
- Scale factor more than 1 => shape gets bigger
- Scale factor less than 1 => shape gets smaller
- Congruent shapes are similar shapes with SF = 1
scale model
scale factor
scale drawing
The scale can be written as a
scale factor, which is the ratio of
the length or size of the drawing
or model to the length of the
corresponding side or part on the
actual object.
Scale Factor needs to be the
This HO gauge model train is a
scale model of a historic train. A
scale model is a proportional
model of a three-dimensional
object. Its dimensions are related
to the dimensions of the actual
object by a ratio called the scale
factor. The scale factor of an HO
gauge model train is 87 .
This means that each dimension of the model is
of the corresponding dimension of the actual
A scale is the ratio between
two sets of measurements.
Scales can use the same units
or different units. The
photograph shows a scale
drawing of the model train.
A scale drawing is a proportional
drawing of an object. Both scale drawings
and scale models can be smaller or larger
than the objects they represent.
If you have ever seen Jurassic
Park, you saw how big the
dinosaurs were compared to the
people. Pretend that they made
a large Human to watch over the
animals. What would be the scale
factor if a 64 inch person was
made to be 160 feet?
The scale factor tells you
how many times bigger than
“normal” that person really is.
You must make all units of
measure the same….
64 inches 64 inches 64 inches
160 feet 160 x 12 1920 inches
Now take the:
64 inches
1920 inches
And simplify
1/30 inches
This means that the person
was created 30 times his
normal size.
The scale factor
of the pool is
1” to 20 yards.

Keep like
units in
the same
Inches = yards
There is more than
one way to set up
a proportion
Cross Multiply!
Use common
 Tom is drawing a blueprint for a rectangular
shed he wants to build. The scale factor is 1
ft. to ¼ inch. If the dimensions of the
blueprint are 1 ¼ in. by 2 inches, what are
the actual dimensions of the shed going to
¾ inch to 1 foot
If the length in inches is 2
¼ inch, what would the
actual length be in feet ?
Footprints of
Scale 1 cm = 1 m
Length of units = 6 m
Scale 1 : 1 000 000
Scale 2 cm = 1 m
When objects are too small or too large to
be drawn or constructed at actual
size, people use a scale drawing or a
The scale drawing of this tree is 1:500
If the height of the tree on paper is 20 inches, what
is the height of the tree in real life?
The scale is the relationship between
the measurements of the drawing or
model to the measurements of the
In real-life, the length of this van may
measure 240 inches. However, the
length of a copy or print paper that you
could use to draw this van is a little bit
less than 12 inches
Map Scales (Legends) are
used to find distances on a
For example, if your map
legend tells you that ½ of
an inch represents 50 miles,
how could you find the
mileage for a 2 inch
distance on the map?
Ratios and proportions can be used to find distances using a scale.
1 inch = 15 miles
The distance from Jacksonville to Smithtown on a map
is 4 inches. How many miles are between these cities?
1 in. = 4 in
15 mi.
The distance between
1n = 60
n = 60
the two cities is
60 miles.

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