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Scale Factor
Real world application
Finding coordinates before / after a dilation
Scale Factor
Real world application
100

What is scale factor?

The scale factor is a number that describes how much a figure is enlarged or reduced

100

A model airplane is built at a scale factor ratio of 1:25. If the wingspan of the actual airplane is 50 feet, what is the wingspan of the model airplane?

2 feet

100
Point A (20, 10) was dilated by a scale factor of 1/2. What are the coordinates of A'?
A' (10, 5)
100

Does a dilation of 5/3 shrink or enlarge (magnify) a figure?

Enlarge (magnify)

100

An architect is designing a scale model of a building that is 120 feet tall. They want the model to be 1/20th the size of the actual building. What will the height of the model be?

6 feet

200

A(3, 6) A' (9, 18) What is the scale factor?

k=3

200

A city map has a scale of 1 inch = 2 miles. If the distance between two landmarks on the map is 4 inches, what is the actual distance between them?

8 miles

200
Point A (2,3), Point B (1, -4), and Point C (1, 1) were dilated by a scale factor of 2. What are the coordinates of A', B', C'?
A'(4,6) B'(2, -8) C'(2, 2)
200
Angle B is 72 degrees. After a dilation of 1/2, what is the measure of angle B'?
72 degrees.
200
  • A map uses a scale factor of 1:50,000. If two cities are 3 inches apart on the map, what is the actual distance between the cities in miles?

Ft per mile----->5280

2.37 miles

300

A(12, 6) A' (2, 1) What is the scale factor?

k=1/6

300

An architect creates a blueprint for a house where 1 inch on the plan represents 10 feet in reality. If a room measures 3 inches by 4 inches on the blueprint, what are the actual dimensions of the room?

30 ft x 40 ft

300

determine the original coordinates

if the scale factor=12 

A'(48, 60) B'(12, 24) C'(12, 36) D'(108, 72)

A(4 , 5) B (1, 2) C( 1, 3), D (9, 6).

300
What is preserved in dilations?
Angle measure
300

A gardener has a plot that measures 40 feet by 30 feet. They want to create a scaled drawing of the plot with a scale factor of 1/4. What will be the area of the scaled drawing?

75 ft^2

400
How do you find scale factor?
Divide the image length by the original length
400

A landscaping company is creating a scale model of a park at a scale of 1:80. If the actual park is 200 meters long, how long will it be in the model?

2.5 meters

400

How do you find your new coordinates when you are dilating?

Multiply the original coordinates by the scale factor.

400

Where might you see dilations or scale factor outside of school?

There is not one right answer

explain

400

A photographer takes a picture of a landscape that is 300 pixels wide. If they want to enlarge the image by a scale factor of 2.5 for printing, what will the width of the printed image be?

750 pixels

500

If a figure is getting larger the scale factor is ________. If a figure is getting smaller the scale factor is ________.

greater than 1, less than 1 but greater than 0

500

In a video game, a character is represented at a scale of 1:10. If the character is 6 inches tall in the game, how tall is the actual character supposed to be in feet?

5 ft 

500

A' (4, 8) B' (2, 5) C' (3,1) Determine the original coordinates if the scale factor is k = 1/2

A(8, 16) B(4, 10) C (6,2)

500

In a school art project, students are asked to create a scaled model of their school. If the actual length of the school building is 120 feet, and the students decide to use a scale factor of 1:10 for their model, what will be the length of the building in the model?

12 ft

500

A designer is creating a floor plan for a living room that measures 18 feet by 15 feet. They want to create a scaled drawing with a scale factor of 1/6. What will be the dimensions of the living room on the drawing?

3ft x 2.5ft