# USING PROPORTIONAL RELATIONSHIPS TO FIND DISTANCE ON A MAP

## About "Using proportional relationships to find distance on a map"

Using proportional relationships to find distance on a map :

A scale drawing is a drawing of a real object that is proportionally smaller or larger than the real object.

A scale is a ratio between two sets of measurements. It shows how a dimension in a scale drawing is related to the actual object.

A map is a scale drawing. The measurements on a map are in proportion to the actual distances.

If 1 inch on a map equals an actual distance of 2 miles, the scale is 1 inch = 2 miles. We can write a scale as a rate to solve problems.

## Using proportional relationships to find distance on a map - Examples

Example 1 :

The distance between two schools on Lehigh Avenue is shown on the map. If the scale is 1 inch = 2 miles, what is the actual distance between the schools ? Solution :

Step 1 :

Write a proportion using the scale as a unit rate. Step 2 :

Use the proportion to find the distance. Because 1 × 3 = 3, multiply 2 by 3.

Hence, the actual distance between the two schools is 6 miles.

Example 2 :

The distance between Sandville and Lewiston is shown on the map. If the scale is 1 inch = 20 miles, what is the actual distance between the towns ? Solution :

Step 1 :

Write a proportion using the scale as a unit rate. Step 2 :

Use the proportion to find the distance. Because 1 × 2.5 = 2.5, multiply 20 by 2.5

Hence, the actual distance between the towns is 50 miles.

Example 3 :

The actual distance between two towns is 90 miles. If the scale is 1 inch = 30 miles, what is the distance between the two towns on the map ?

Solution :

Step 1 :

Write a proportion using the scale as a unit rate.

Actual distance / map distance  =  30/1  =  90 / ?

Step 2 :

Use the proportion to find the distance.

30 / 1  =  (30 x 3) / (1 x 3)  =  90 / 3

Because 30 × 3 = 90, multiply 1 by 3

Hence, the distance between the towns on the map is 3 inches

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