Maps and Scale Drawings
What You'll Learn
To use maps, as in Example 2
Solving Problems Involving Scale
Ais an enlarged or reduced drawing of an object that is similar to an actual object. Maps and floor plans are smaller than the actual size. A scale drawing of a human cell is larger than the actual size.
On a map, the equal sign in 1 in. = 30 mi does not mean that the two quantities are equal, as it would in an equation.
Ais the ratio that compares a length in a drawing to the corresponding length in the actual object. If a 30-mile road is 1 in. long on a map, you can write the scale of the map in these three ways:
Using a Scale Drawing
You have a scale drawing of a boat. The length of the boat on the drawing is 3 cm. What is the actual length of the boat?
Write the scale of the drawing, 1 cm = 1.5 m, as . Then write a proportion in which each ratio compares centimeters to meters.
Let n represent the actual length of the boat.
The actual length of the boat is 4.5 m.
You can use proportions and a map's scale to find actual distances.
Real-World Problem Solving
GeographyFind the actual distance from Charlotte to Winston-Salem.
- Use a centimeter ruler to find the map distance from Charlotte to Winston-Salem. The map distance is about 1.6 cm.
- Use a proportion to find the actual distance. Let n represent the actual distance.
The actual distance from Charlotte to Winston-Salem is about 120 km.
You can use the GCF of two numbers to find the scale of a drawing or a model.
Finding the Scale
ModelsRefer to the model boxcar shown at the right. The actual length of a boxcar is 609 in. What is the scale of the model?
The scale is 1 in. : 87 in.
Investigation:Making a Scale Drawing
Make a scale drawing of your classroom.
- Using a meter stick or yardstick, measure the classroom. Measure the length and width of the room and anything else you think you need.
- Choose a scale large enough to produce a good drawing, but small enough to fit on your paper.
- Complete your drawing. Include the scale.
Exercises Click here to view the Exercises for this lesson.
Investigation Click here to view the Investigation: Plan a Trip.