1. Course 3 5-8 Scale Drawings and Scale Models Warm Up Evaluate the following for x = 16. 1. 3x2. x Evaluate the following for x =. 3. 10x4. x 4812 4 3 4 2 5 1 4 1 10

2. Course 3 5-8 Scale Drawings and Scale Models Problem of the Day An isosceles triangle with a base length of 6 cm and side lengths of 5 cm is dilated by a scale factor of 3. What is the area of the image? 108 cm 2

3. Course 3 5-8 Scale Drawings and Scale Models Learn to make comparisons between and find dimensions of scale drawings, models, and actual objects. TB P. 252-255

4. Course 3 5-8 Scale Drawings and Scale Models Vocabulary scale drawing scale scale model reduction enlargement

5. Course 3 5-8 Scale Drawings and Scale Models A scale drawing is a two-dimensional drawing that accurately represents an object. The scale drawing is mathematically similar to the object. A scale gives the ratio of the dimensions in the drawing to the dimensions of the object. All dimensions are reduced or enlarged using the same scale. Scales can use the same units or different units.

6. Course 3 5-8 Scale Drawings and Scale Models ScaleInterpretation 1:201 unit on the drawing is 20 units. 1 cm:1 m1 cm on the drawing is 1 m. in. = 1 ftin. on the drawing is 1 ft. 1414 1414

7. Course 3 5-8 Scale Drawings and Scale Models A. The length of an object on a scale drawing is 2 cm, and its actual length is 8 m. The scale is 1 cm: __ m. What is the scale? Additional Example 1: Using Proportions to Find Unknown Scales or Lengths 1 cm x m = 2 cm 8 m 1  8 = x  2Find the cross products. 8 = 2x Solve the proportion. The scale is 1 cm:4 m. 4 = x Set up proportion using scale length. actual length

8. Course 3 5-8 Scale Drawings and Scale Models The scale a:b is read “a to b.” For example, the scale 1 cm:4 m is read “one centimeter to four meters.” Reading Math

9. Course 3 5-8 Scale Drawings and Scale Models Under a 1000:1 microscope view, an amoeba appears to have a length of 8 mm. What is its actual length? Additional Example 2: Life Sciences Application scale length actual length 1000  x = 1  8Find the cross products. x = 0.008 The actual length of the amoeba is 0.008 mm. 1000 1 = 8 mm x mm Solve the proportion.

10. Course 3 5-8 Scale Drawings and Scale Models A scale model is a three-dimensional model that accurately represents a solid object. The scale model is mathematically similar to the solid object.

11. Course 3 5-8 Scale Drawings and Scale Models A model of a 27 ft tall house was made using a scale of 2 in.:3 ft. What is the height of the model? Additional Example 3: Finding Unknown Dimensions Given Scale Factors First find the scale factor. The scale factor for the model is. Now set up a proportion. 1 18 2 in. 3 ft = 2 in. 36 in. = 1 in. 18 in. = 1 18 324 = 18h Convert: 27 ft = 324 in. Cross multiply. 18 = h The height of the model is 18 in. Solve for the height. 1 18 = h in. 324 in.

12. Course 3 5-8 Scale Drawings and Scale Models A DNA model was built using the scale 5 cm: 0.0000001 mm. If the model of the DNA chain is 20 cm long, what is the length of the actual chain? Find the scale factor. Additional Example 4: Life Science Application The scale factor for the model is 500,000,000. This means the model is 500 million times larger than the actual chain. 5 cm 0.0000001 mm 50 mm 0.0000001 mm == 500,000,000

13. Course 3 5-8 Scale Drawings and Scale Models Additional Example 4 Continued 500,000,000 1 20 cm x cm =Set up a proportion. 500,000,000x = 1(20) x = 0.00000004 The length of the DNA chain is 4  10 -7 cm. Cross multiply. Solve for the length.

14. Course 3 5-8 Scale Drawings and Scale Models 1. What is the scale of a drawing in which a 9 ft wall is 6 cm long? 2. Using a in. = 1 ft scale, how long would a drawing of a 22 ft car be? 3. The height of a person on a scale drawing is 4.5 in. The scale is 1:16. What is the actual height of the person? Lesson Quiz 5.5 in. 1 cm = 1.5 ft 72 in. 1 4