7-4 Scale Drawings p Indicator – M4 Solve problems involving scale factors
7-4 Scale Drawings p When actual distances are very far or small, they may be represented more conveniently with proportionally scale drawings or models. This process involves a scale (ratio) which is used to form a proportion. A map is an example of a scale drawing. The scale on a map is the ratio of the distance on the map to the actual distance.
7-4 Notes A Scale Drawing/Model represents something that is too large or too small to be drawn/built at actual size. The Scale gives the relationship between the drawing/model measure and the actual measure. Scale Factor- is when you convert the scale to a common unit and simplify
Scale factor If the scale on a map is ¼ inch represents 1 foot, what is the scale factor? Step 1: Write the scale as a ratio scale ¼in actual 1 ft Step 2 : Change to a common unit of measure scale ¼in actual 12 in Step 3: Simplify 1/4 ÷ 12 1/4 x 1/12 = 1/48 the scale factor is 1/48 of the actual
Example 1 Tracy and Tyrone are planning a hiking trip. On the map, their route is 7.5 cm long. The map scale says that 1 cm represents 3 km. What is the actual length of their hike? Let d represent the hiking distance. Write and solve a proportion. Map distance 1 cm = 7.5 cm Actual distance 3 km = d 1 × d = 3 × 7.5 d = 22.5 The actual length 22.5 km.
Example 2 The scale of a blueprint is 1 in. = 4 ft. If the actual width of a porch is 16 ft, what is the width on the blueprint? Let w represent the porch width. Write and solve a proportion. Blueprint width 1 in. = w_ actual width 4 ft = 16 ft 4 × w = 1 × 16 4w = w = 4 The width of the blueprint is 4 inches. Cross-multiply Isolate the variable Write a sentence!
On this map, each grid unit represents 50 yards. Find the distance from Patrick’s Point to Agate Beach.
You Try Find the scale factor of the scale 2cm = 1 m A blue print is drawn so that ¼ in is 1 foot of the original size. If the actual kitchen is 14 feet long, how long will it appear on the print?