7-4 Scale Drawings p. 304-308

Indicator – M4 Solve problems involving scale factors

7-4 Scale Drawings p. 304-308

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 ftStep 2 : Change to a common unit of measure

scale ¼inactual 12 in

Step 3: Simplify1/4 ÷ 121/4 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 = 16 4 4

w = 4The 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?