Name: __________________________________________
Period: _______
Date: _________________
Math 7 – Section 1.4 – Scale Drawings
**Goal: I can use scales & scale factors to draw figures and find missing side lengths**
Vocabulary:
1) _____________________ - A drawing that shows an object with sizes reduced or enlarged by a certain
factor.
2) _____________________ - The ratio of a length on a map or model to the actual object.
3) _____________________ - The ratio of corresponding sides in two similar figures.
4) _____________________ - Sides that are in the same location on two figures.
Let’s Explore!
A scale factor is a multiplier applied to lengths to make an image enlarged (made bigger) or reduced
(made smaller).
Step 1: When a scale factor of 3 is applied to an image, it results in an image where each side length is
3 times the length of the original image. Let’s apply a scale factor of 3 to the image below and draw the
resulting image:
Step 2: Does a scale factor of 3 make an enlargement or a reduction of the original image?
Step 3: Use the same shape above to create another scale drawing using a scale factor of ½ instead. Is
this new drawing an enlargement or a reduction of the original image?
Conclusion:
Example 1: A model train has a length of 6 cm and a scale of 1 cm : 8 ft. Answer the following:
a) What is the length of the actual train?
Step 1: Write a proportion using the given scale (in fraction form) and the 1 given measurement:
*numerators & denominators must have the same units*
Step 2: Solve the proportion using cross-multiplication:
b) What is the height of the actual train?
EXTRA PRACTICE: A map has a scale of 1 inch : 9 miles. Use the given distance on the map to find the
actual distance
a) 5 inches
b) 8 inches
Example 2: A scale factor of 2 is applied to the figure below. Draw the resulting figure:
**A scale factor of 2 is an enlargement where each side length is 2
times as large as the original object**
1) Count the units on each side length of the shape and label them
2) Multiply each side length by 2. Show your work below:
3) Draw the resulting figure with the new side lengths. The general
shape of the figure should look the same.
Example 3: Use the same image above and apply a scale factor of 1/2. Draw the resulting figure on the
grid:
Now let’s work backwards to determine the scale factor given two shapes:
Example 4: What scale factor would be applied to figure M to produce figure G?
To find the scale factor comparing
Figure M and Figure G, write a ratio
of 2 corresponding side lengths
comparing M : G
(Any two side lengths, one from each
triangle, can be used as long as they are
corresponding sides)
Make sure to simplify the ratio!
The scale factor to compare these two figures can be written as _________ or _________ depending on if you are
applying the scale factor to the larger figure to create a reduction or to the smaller figure to create an enlargement.
**To go from Figure M (larger) to Figure G (smaller) would be a reduction and the scale factor would be _____.
Example 5: What scale factor would be applied to Figure P to produce Figure Q?
1
Example 6: Figure K is a scale image of Figure T, as shown. The scale that maps Figure K onto Figure T is 1 ∶ 3 2
What is the area of Figure T?
Find the height of Figure T by multiplying the height
1
of Figure K by 3 2.
Find the length of the base of Figure T by
1
multiplying the base of Figure K by 3 .
2
Now that you have the base and height of Figure T, you can find the area of the triangle. Remember, the formula
1
for area of a triangle is 𝐴 = 2 𝑏ℎ :
EXTRA EXAMPLE: Square B has side lengths of 5 inches. Square H is formed by applying a scale factor of 3 to
Square B. What is the area of Square H?
PRACTICE:
1) A map has a scale of 2 inches : 5 miles. Use the given distance on a map to find the actual distance.
a) 4 inches
b) 7 inches
c) 1 ft 3 inches (hint: how many total inches?)
2) An airplane model has a scale of 1 inch : 12 feet. Use the given lengths on the actual airplane to find
the length of that part on the model.
a) 48 feet
b) 72 feet
c) 102 feet
3) What was the scale factor that was applied to Triangle C to create Triangle D?