Learn to understand ratios and proportions in scale drawings

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Presentation transcript:

Learn to understand ratios and proportions in scale drawings Learn to understand ratios and proportions in scale drawings. Learn to use ratios and proportions with scale.

Vocabulary scale drawing scale factor scale model scale

A scale drawing is a proportional two-dimensional drawing of an object. Its 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. 1 87 1 87

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 photograph shows a scale drawing of the model train.

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 18 Wing span (in.)‏ 2 12 Length (in.)‏ Blueprint Model Aircraft blueprint length aircraft length 2 12 = Write a ratio using one of the dimensions. 1 6 = Simplify. The scale factor is . This is reasonable because of the length of the model is 3 in. The length of the blueprint is 2, which is less. is less than . 1 6 4

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.

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(in) D (mi) = 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.