Table of Contents

- Working with Scale
- Measuring Distance Using a Graphic Scale
- Calculating Slope When Determining Distance
- Converting Map Distance to Ground Distance Using a Representative Fraction (RF)
- Determining Scale Using a Representative Fraction

# Determining Scale Using a Representative Fraction

It is also possible to determine an unknown scale by using the representative fraction from a source with a known scale, such as a map.

For example, suppose you acquired an old aerial photograph but were unsure of the scale. You could use the scale from a known source, such as a map, to determine the scale of the photo.

Recall the definition of scale. In this course, the ratio of map distance over ground distance defines **scale**.

To determine the scale of the old photograph, you need to know how the distance on the photo relates to the distance on the ground.

To start, measure the distance of a prominent feature on the photo that you could also identify on a map. In this instance, the let us assume that the width of the divide in the oxidation pond, when measured on the photograph, is **six inches**.

By measuring of the distance on the photograph, you have half of the ratio for determining scale, the **photo distance**.

Next, determine how far this distance represents on earth, which we call **ground distance**. Let us assume that the same distance, when measured on the Arcata South USGS Topographic Quadrangle is **one inch**.

## Skill Drill: Converting Map Distance to Ground Distance Using a Representative Fraction (RF)

In the previous step, you learned how to convert map distance to ground distance using a Representative Fractions (RF). The RF for the Arcata South USGS Topographic Quadrangle is **1:24000**.

On a separate piece of paper, write down the answers to the following questions:

- What is the ground distance of the width of the oxidation pond, given that the distance on the map was 1 inch and the map RF is 1:24,000?

- Based on your answer to question 8 and the definition of scale, what is the scale of the photo? Be sure to reduce the fraction so that you have the number 1 in the numerator and can represent the ratio as 1:x.
- What would be the best way to express the scale of the old photograph as a
**word statement**? - Is the old photograph larger or smaller in scale than the Arcata South USGS Topographic Quadrangle?