Warm Up Write each fraction in the simplest form. 4 48 1 12 9 135 1 15 2. 1. 3. Scale 2.5 cm = 50 miles What is the distance in miles if you measure 4.75 cm? 95 miles 4. Scale 1.75 in = 21 miles What is the distance in miles if you measure 4 in? 48 miles

I CAN … use a scale factor to increase or decrease the size of an object, So that I can make a scale drawing of an object!

Vocabulary scale drawing scale factor scale model scale

A scale drawing is a proportional two-dimensional drawing of an object A scale drawing is a proportional two-dimensional drawing of an object. A blueprint is an example of this.

For example, if a drawing of a building has A scale drawings dimensions are related to the dimensions of the actual object by a ratio called the scale factor. For example, if a drawing of a building has a scale factor of , this means that each dimension of the drawing is of the corresponding dimension of the actual building. A scale factor is always the ratio of the model’s dimensions to the actual object’s dimensions. Caution! model actual 1 10 1 10

A scale model is a proportional three- dimensional model of an object. A scale is the ratio between two sets of measurements. Scales can use the same units or different units. The Iron Man drawing shows a scale drawing of a real Iron Man suit.

Since the scale is a ratio, we can use proportional thinking to find actual distance based on a measurement, usually in inches or centimeters, from the map.

The map below shows the distance from Denver to Atlanta in centimeters.

Understand the Problem According to the scale, what is the actual distance from Denver to Atlanta? 1 Understand the Problem Rewrite the question as a statement. Find distance the between the two cities in miles. List the important information: 3 cm on the map is 900 miles.

2 Make a Plan Set up a proportion using the given information. Let x represent the distance in miles. 3 centimeters 900 miles 4 centimeters x miles centimeters miles =

The cross products are equal. Solve 3 3 900 4 x Write the proportion. = 900 · 4 = 3 · x The cross products are equal. 3600 = 3x Multiply. 3600 3 3x 3 Divide each side by 3 to isolate the variable. = 1200 = x The scale distance of 4 cm represents 1200 actual miles.

4 Look Back 900 · 4 = 3600 3 900 4 1200 = 3 · 1200 = 3600 The cross products are equal, so 1200 is the answer.

4 Alternate Method Another way to solve this problem is to think about how many miles would be covered in 1 cm. 900 miles 3 cm 300 miles 1 cm = If 1 cm is 300 miles, then how many miles would be covered in 4 cm? 300 · 4 = 1200 miles

Additional Example 1: Finding a Scale Factor Identify the scale factor. 13.5 108 Width (in.)‏ 18 144 Length (in.)‏ Blueprint Room blueprint length room length 18 144 Write a ratio using one of the dimensions. = 1 8 = Simplify. A scale factor is always the ratio of the model’s dimensions to the actual object’s dimensions. Caution! 1 8 The scale factor is .

Check It Out: Example 1 Identify the scale factor. 3 cm 18 ft. Wing span‏ 2 cm 12 ft. Length‏ Blueprint Aircraft blueprint length aircraft length 2 12 = Write a ratio using one of the dimensions. 1 6 = Simplify. blueprint wing span aircraft wing span 3 18 = Write a ratio using one of the dimensions. 1 6 = Simplify.

Additional Example 2: Using Scale Factors to Find Unknown Lengths A photograph was enlarged and made into a poster. The poster is 20.5 inches by 36 inches. The scale factor is . Find the size of the photograph. 5 1 poster photo 5 1 Think: = 36 l 5 1 = Write a proportion to find the length l. 5l = 36 Find the cross products. l = 7.2 Divide.

Additional Example 2 Continued A photograph was enlarged and made into a poster. The poster is 20.5 inches by 36 inches. The scale factor is . Find the size of the photograph. 5 1 poster photo 5 1 Think: = 20.5 w 5 1 Write a proportion to find the width w. = 5w = 20.5 Find the cross products. w = 4.1 Divide. The photo is 7.2 in. long and 4.1 in. wide.

factor is . Find the size of the dollhouse. 1.5 1 Check It Out: Example 2 Mary’s father made her a dollhouse which was modeled after the blueprint of their home. The blueprint is 24 inches by 45 inches. The scale factor is . Find the size of the dollhouse. 1.5 1 dollhouse blueprint 1.5 1 Think: = l 45 = 1.5 1 Write a proportion to find the length l. Find the cross products. l = 45 · 1.5 l = 67.5 Multiply.

Check It Out: Example 2 Continued Mary’s father made her a dollhouse which was modeled after the blueprint of their home. The blueprint is 24 inches by 45 inches. The scale factor is . Find the size of the dollhouse. 1.5 1 dollhouse blueprint 1.5 1 Think: = w 24 1.5 1 Write a proportion to find the width w. = w = 24 · 1.5 Find the cross products. w = 36 Multiply. The dollhouse is 67.5 inches long and 36 inches wide.

Additional Example 3: Measurement Application On a road map, the distance between Pittsburgh and Philadelphia is 7.5 inches. What is the actual distance between the cities if the map scale is 1.5 inches = 60 miles? Let d be the actual distance between the cities. 1.5 60 7.5 d = Write a proportion. 1.5 · d = 60 · 7.5 Find the cross products. 1.5d = 450 Multiply. 1.5d 1.5 450 1.5 = Divide both sides by 1.5. d = 300 The distance between the cities is 300 miles.

Check It Out: Example 3 On a road map, the distance between Dallas and Houston is 7 inches. What is the actual distance between the cities if the map scale is 1 inch = 50 kilometers? Let d be the actual distance between the cities. 1 50 7 d = Write a proportion. 1 · d = 50 · 7 Find the cross products. 1d = 350 Multiply. d = 350 The distance between the cities is 350 kilometers.

Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems

Lesson Quiz: Part I Identify the scale factor. 1. 8 1,824 Height (in.)‏ Model Statue of Liberty 1 228 2. On a scale drawing, a kitchen wall is 6 inches long. The scale factor is . What is the length of the actual wall? 1 24 144 inches, or 12 feet

Lesson Quiz: Part II 3. On a road map, the distance from Green Bay to Chicago is 11 cm. What is the actual distance between the cities if the map scale is 3 cm = 90 km? 330 km

Lesson Quiz for Student Response Systems 1. Identify the scale factor. A. C. 10 B. D. 20 Fish Model Length (cm) 120 12 1 20 1 10

Lesson Quiz for Student Response Systems 2. On a scale drawing, the height of a building is 60 inches. The scale factor is . What is the height of the actual building? A. 240 in., or 20 ft B. 300 in., or 25 ft C. 600 in., or 50 ft D. 900 in., or 75 ft 1 15

Lesson Quiz for Student Response Systems 3. On a road map, the distance from Washington, DC to New York is 15 cm. What is the actual distance between the cities if the map scale is 3 cm = 50 mi? A. 150 mi B. 200 mi C. 250 mi D. 300 mi