Over Lesson 7 6 Determine whether the dilation from Figure A to Figure B is an enlargement or a reduction. Then find the scale factor of the dilation.
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1 Five-Minute Check (over Lesson 7 6) CCSS Then/Now New Vocabulary Example 1: Use a Scale Drawing Example 2: Find the Scale Example 3: Real-World Example: Construct a Scale Model 1
2 Over Lesson 7 6 Determine whether the dilation from Figure A to Figure B is an enlargement or a reduction. Then find the scale factor of the dilation. The coordinates of the vertices of two triangles are listed in the table. What is the scale factor of the dilation from ABC to XYZ? Over Lesson 7 6 Determine whether the dilation from Figure A to Figure B is an enlargement or a reduction. Then find the scale factor of the dilation. A. enlargement; 7 4 B. enlargement; 4 7 C. reduction; D. reduction;
3 Over Lesson 7 6 Determine whether the dilation from Figure A to Figure B is an enlargement or a reduction. Then find the scale factor of the dilation. A. enlargement; B. enlargement; C. reduction; D. reduction; Over Lesson 7 6 The coordinates of the vertices of two triangles are listed in the table. What is the scale factor of the dilation from ABC to XYZ? A. B C. 2 D. 3 3
4 Content Standards G.MG.3 Apply geometric methods to solve problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios). Mathematical Practices 4 Model with mathematics. 7 Look for and make use of structure. You used scale factors to solve problems with similar polygons. Interpret scale models. Use scale factors to solve problems. 4
5 scale model scale drawing scale Use a Scale Drawing MAPS The distance between Boston and Chicago on a map is 9 inches. If the scale of the map is 1 inch: 95 miles, what is the actual distance from Boston to Chicago? Method 1 Write and solve a proportion. Let x represent the distance between Boston and Chicago. 1 x = 95 9 x = 855 miles 5
6 Use a Scale Drawing MAPS The distance between Boston and Chicago on a map is 9 inches. If the scale of the map is 1 inch: 95 miles, what is the actual distance from Boston to Chicago? Method 2 Write and solve an equation. distance = distance = 9 9 distance = 95 9 distance = 855 MAPS The distance between Cheyenne, WY, and Tulsa, OK, on a map is 8 inches. If the scale of the map is 1 inch : 90 miles, what is the actual distance from Cheyenne to Tulsa? A. 800 miles B. 900 miles C. 630 miles D. 720 miles 6
7 Find the Scale A. SCALE MODEL A miniature replica of a fighter jet is 4 inches long. The actual length of the jet is 12.8 yards. What is the scale of the model? To find the scale, write the ratio of a replica length to a corresponding actual length. Answer: The scale of the model is 1 inch : 3.2 yards Find the Scale B. SCALE MODEL A miniature replica of a fighter jet is 4 inches long. The actual length of the jet is 12.8 yards. How many times as long as the actual is the model jet? To answer this question, find the (unitless) scale factor of the model = = Answer: The scale factor is : 1. That is, the actual jet is times as long as the model. 7
8 A. SCALE MODEL A miniature replica of a fire engine is 9 inches long. The actual length of the fire engine is 13.5 yards. What is the scale of the replica? A. 2 in. : 3 yd B. 1 in. : 3 yd C. 2 in. : 5 yd D. 3 in. : 4 yd B. SCALE MODEL A miniature replica of a fire engine is 9 inches long. The actual length of the fire engine is 13.5 yards. How many times as long as the model is the actual fire engine? A. 48 B. 54 C. 60 D. 63 8
9 Construct a Scale Model SCALE DRAWING Cole is making a scale model of his classroom on an 11-by-17 inch sheet of paper. If the classroom is 20 feet by 32 feet, choose an appropriate scale for the drawing and determine the drawing s dimensions. The actual classroom is 20 feet wide. 20 feet 11 inches = 1.8 feet per inch The actual classroom is 32 feet long. 32 feet 17 inches = 1.8 feet per inch A scale of 1 inch = 2 feet would be appropriate. So, for every inch on the paper p, let the actual measure a be 2 feet. Write this as an equation. Construct a Scale Model SCALE DRAWING Cole is making a scale model of his classroom on an 11-by-17 inch sheet of paper. If the classroom is 20 feet by 32 feet, choose an appropriate scale for the drawing and determine the drawing s dimensions. width: length: w = 2 p 20 = 2 p 10 = p l = 2 p 32 = 2 p 16 = p A scale of 1 inch = 2 feet would be appropriate. Answer: So, for every 1 in. inch : 2 ft; on 10 the in. paper wide, p, 16 let in. the long actual measure a be 2 feet. Write this as an equation. 9
10 ARCHITECTURE Lauren is an architect making a scale model of a house in a 15-by-26 inch display. If the house is 84 feet by 144 feet, what would be the dimensions of the model using a scale of 1 in. : 6 ft? A. 14 in. 24 in. B. 14 in. 25 in. C. 15 in. 25 in. D. 15 in. 26 in. 10
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Example. h + 8 < -13 and b 4 > -6 Multiplying and dividing inequalities
Unit 2 (continued): Expressions and Equations 2 nd 9 Weeks Suggested Instructional Days: 10 Unit Summary (Learning Target/Goal): Use properties of operations to generate equivalent expressions. CCSS for