7.5 Scale Drawings

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7.5Scale DrawingsHow can you enlarge or reduce a drawingproportionally?1ACTIVITY: Comparing MeasurementsWork with a partner. The diagram shows a food court at a shopping mall.Each centimeter in the diagram represents 40 meters.a. Find the length and the width ofthe drawing of the food court.length:cmwidth:cmb. Find the actual length and widthof the food court. Explain how youfound your answers.length:mwidth:mdrawing lengthactual lengthc. Find the ratios —— anddrawing widthactual width——. What do you notice?2ACTIVITY: Recreating a DrawingWork with a partner. Draw the food court in Activity 1 on the grid paperso that each centimeter represents 20 meters.COMMONCOREGeometryIn this lesson, you will use scale drawings tofind actual distances. find scale factors. use scale drawings tofind actual perimetersand areas. recreate scale drawingsat a different scale.Learning Standard7.G.1298Chapter 7a. What happens to the size of the drawing?b. Find the length and the width of your drawing. Compare these dimensionsto the dimensions of the original drawing in Activity 1.Constructions and Scale Drawings

3ACTIVITY: Comparing MeasurementsWork with a partner. The diagram shows a sketch of a painting.Each unit in the sketch represents 8 inches.a. Find the length and the width of the sketch.length:unitswidth:unitsb. Find the actual length and width of the painting.Explain how you found your answers.length:in.width:sketch lengthactual lengthin.sketch widthactual widthc. Find the ratios —— and ——.What do you notice?4MathPracticeSpecify UnitsHow do you knowwhether to use feetor units for eachmeasurement?ACTIVITY: Recreating a DrawingWork with a partner. Let each unit in the gridpaper represent 2 feet. Now sketch the paintingin Activity 3 onto the grid paper.a. What happens to the size of the sketch?b. Find the length and the width of your sketch.Compare these dimensions to the dimensionsof the original sketch in Activity 3.5. IN YOUR OWN WORDS How can you enlarge or reduce a drawingproportionally?6. Complete the table for both the food court and the painting.Actual ObjectOriginal DrawingYour DrawingPerimeterAreaCompare the measurements in each table. What conclusions can you make?7. RESEARCH Look at some maps in your school library or on theInternet. Make a list of the different scales used on the maps.8. When you view a map on the Internet, how does the scale changewhen you zoom out? How does the scale change when you zoom in?Use what you learned about enlarging or reducing drawingsto complete Exercises 4 7 on page 303.Section 7.5Scale Drawings299

7.5LessonLesson TutorialsKey VocabularyScale Drawings and Modelsscale drawing, p. 300scale model, p. 300scale, p. 300scale factor, p. 301A scale drawing is a proportional, two-dimensional drawing of an object.A scale model is a proportional, three-dimensional model of an object.ScaleThe measurements in scale drawings and models are proportional tothe measurements of the actual object. The scale gives the ratiothat compares the measurements of the drawing or model withthe actual measurements.Study Tip1 in.10 miScales are writtenso that the drawingdistance comes first inthe ratio.drawing distance—1 in. : 10 miactual distancedrawingEXAMPLE1actualFinding an Actual DistanceWhat is the actual distance d between Cadillac and Detroit?Marquette1 cm : 50 miEscanabaStep 1: Use a centimeter ruler tofind the distance on the mapbetween Cadillac and Detroit.The map distance is about3.5 centimeters.Step 2: Use the scale to write and solvea proportion.map distance1 cm3.5 cm— —50 mid miactual distance AlpenaTraverse Cityd 50 3.5Cross Products Propertyd KalamazooAnnArborDetroitSo, the distance between Cadillac and Detroit is about 175 miles.1. What is the actual distance between Traverse City and Marquette?Exercises 8–11300Chapter 7Constructions and Scale Drawings

EXAMPLE2Finding a Distance in a ModelThe liquid outer core of Earth is 2300 kilometers thick. A scalemodel of the layers of Earth has a scale of 1 in. : 500 km. How thickis the liquid outer core of the model?A0.2 in. CrustLiquidoutercoreB 4.6 in. 1 in.500 kmC 0.2 km model thicknessx in.2300 km— —Solidinnercore1 in.500 km—actual thicknessx in.2300 km 2300 km —2300 km 4.6 xMantleD4.6 km Multiplication Propertyof EqualitySimplify.So, the liquid outer core of the model is 4.6 inches thick. The correctanswer is B .2. The mantle of Earth is 2900 kilometers thick. How thick is themantle of the model?A scale can be written without units when the units are the same. A scalewithout units is called a scale factor.EXAMPLE3Finding a Scale FactorA scale model of the Sergeant Floyd Monument is 10 inches tall.The actual monument is 100 feet tall.a. What is the scale of the model?model heightactual height10 in.100 ft1 in.10 ft—— — —The scale is 1 in. : 10 ft.b. What is the scale factor of the model?Write the scale with the same units. Use the fact that 1 ft 12 in.1 in.10 ft1 in.120 in.1120scale factor — — —The scale factor is 1 : 120.Exercises 12–163. A drawing has a scale of 1 mm : 20 cm. What is the scale factorof the drawing?Section 7.5Scale Drawings301

EXAMPLE4Finding an Actual Perimeter and AreaThe scale drawing of a computer chip helps you see the individualcomponents on the chip.a. Find the perimeter and the area of the computer chip inthe scale drawing.When measured using a centimeter ruler, the scale drawing of thecomputer chip has a side length of 4 centimeters.So, the perimeter of the computer chip in thescale drawing is 4(4) 16 centimeters, and the areais 42 16 square centimeters.1 cm : 2 mmb. Find the actual perimeter and area of the computer chip.1 cm2 mmdrawing distance4 cms mm— —actual distance s 2 4Cross Products Propertys 8Multiply.The side length of the actual computer chip is 8 millimeters.So, the actual perimeter of the computer chip is4(8) 32 millimeters, and the actual area is82 64 square millimeters.drawing perimeteractual perimeterdrawing areaactual areac. Compare the ratios —— and —— tothe scale factor.Use the fact that 1 cm 10 mm.Study Tip1 cm2 mm10 mm2 mm51scale factor — — —The ratios tell you thatthe perimeter of thedrawing is 5 timesthe actual perimeter,and the area of thedrawing is 52 25times the actual area.drawing perimeteractual perimeter16 cm32 mm1 cm2 mm51—— — — —drawing areaactual area16 cm264 mm1 cm24 mm() ()1 cm 25 2 —2 mm1—— —2 —2 —So, the ratio of the perimeters is equal to the scale factor,and the ratio of the areas is equal to the square of thescale factor.Exercises 22 and 23302Chapter 74. WHAT IF? The scale of the drawing of the computerchip is 1 cm : 3 mm. How do the answers in parts (a)–(c)change? Justify your answer.Constructions and Scale Drawings

Exercises7.5Help with Homework1. VOCABULARY Compare and contrast the terms scale and scale factor.2. CRITICAL THINKING The scale of a drawing is 2 cm : 1 mm. Is the scale drawinglarger or smaller than the actual object? Explain.3. REASONING How would you find the scale factor of a drawing that shows alength of 4 inches when the actual object is 8 feet long?6) 39 (- 3) 3 (- 9) 4 (- 1)9 (-Use the drawing and a centimeter ruler. Each centimeter in the drawing represents 5 feet.4. What is the actual length of theflower garden?5. What are the actual dimensions ofthe rose bed?perennial bedrose bedtulip bedperennialbed6. What are the actual perimeters of theperennial beds?7. The area of the tulip bed is whatpercent of the area of the rose bed?Use the map in Example 1 to find theactual distance between the cities.18. Kalamazoo and Ann Arbor9. Lansing and Flint10. Grand Rapids and Escanaba11. Saginaw and AlpenaFind the missing dimension. Use the scale factor 1 : 12.Item2ModelActualin.3 12.MattressLength: 6.25 in.13.CorvetteLength:14.Water towerDepth: 32 cmDepth:m15.WingspanWidth: 5.4 ftWidth:yd16.Football helmetDiameter:Length:in.mmLength: 15 ftDiameter: 21 cm17. ERROR ANALYSIS A scale is 1 cm : 20 m. Describe andcorrect the error in finding the actual distance thatcorresponds to 5 centimeters. Section 7.51 cm20 mxm5 cm— —x 0.25 mScale Drawings303

Use a centimeter ruler to measure the segment shown. Find the scale of the drawing.18.19.120 mIrisCorneaPupilLens24 mmVitreoushumor20. REASONING You know the length and the width of a scale model. Whatadditional information do you need to know to find the scale of the model?16 ft21. OPEN-ENDED You are in charge of creatinga billboard advertisement with thedimensions shown.a. Choose a product. Then design thebillboard using words and a picture.8 fttb. What is the scale factor of your design?YOUR AD HERE4 22. CENTRAL PARK Central Park is a rectangular park in New York City.1 cm : 320 ma. Find the perimeter and the area of Central Park in the scale drawing.b. Find the actual perimeter and area of Central Park.23. ICON You are designing an icon for a mobile app.a. Find the perimeter and the area of the icon inthe scale drawing.b. Find the actual perimeter and area of the icon.24. CRITICAL THINKING Use the results of Exercises 22and 23 to make a conjecture about the relationshipbetween the scale factor of a drawing and the ratiosdrawing perimeteractual perimeterdrawing areaactual area—— and ——.304Chapter 7Constructions and Scale Drawings1 cm : 2.5 mm

Recreate the scale drawing so that it has a scale of 1 cm : 4 m.26.25.1 cm : 2 m1 cm : 8 mThe shuffleboard diagram hasa scale of 1 cm : 1 ft. Find theactual area of the region.27. red region28. blue region29. green regionReduced Drawing of Blueprint30. BLUEPRINT In a blueprint, each square has a side length14of — inch.Bedrooma. Ceramic tile costs 5 per square foot. How muchwould it cost to tile the bathroom?Livingroomb. Carpet costs 18 per square yard. How much wouldit cost to carpet the bedroom and living room?Bathroom1 in. : 16 ftc. Which has a greater unit cost, the tile or the carpet?Explain.31.Modeling You are making a scale model of the solar system. The radiusof Earth is 6378 kilometers. The radius of the Sun is 695,500 kilometers. Is itreasonable to choose a baseball as a model of Earth? Explain your reasoning.Plot and label the ordered pair in a coordinate plane. (Skills Review Handbook)32. A( 4, 3)33. B(2, 6)35. D( 3, 7)34. C(5, 1)36. MULTIPLE CHOICE Which set of numbers is ordered from least to greatest?(Section 6.2)A 720—, 32%, 0.453B 17%, 0.21, — 257C 0.88, —, 93% 8Section 7.511D 57%, —, 5.7 16Scale Drawings305

actual distance drawing distance drawing actual EXAMPLE 1 Finding an Actual Distance What is the actual distance d between Cadillac and Detroit? Step 1: Use a centimeter ruler to fi nd the distance on the map between Cadillac and Detroit. The map distance is about 3.5 centimeters. Step 2: Use the scale to write and solve a proportion. 1 cm .

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