Define scale. 2. What type of scale is used in the map? Explain. 3. Calculate the straight-line distance between Vryheid and Underberg.

Here are the solutions to the questions:

QUESTION ONE

1.1

Scale, in the context of a map, is the ratio between a distance measured on the map and the corresponding actual distance on the ground. It indicates how much the real world has been reduced to fit on the map.

1.2

The type of scale used in the map is a ratio scale (also known as a representative fraction or RF scale), indicated by "1:4 500 000".
This means that 1 unit of distance on the map represents 4,500,000 of the same units of distance on the actual ground. For example, $1 \text{ cm}$ on the map corresponds to $4,500,000 \text{ cm}$ (or $45 \text{ km}$) in reality.

1.3

Step 1: Determine the real-world equivalent of $1 \text{ cm}$ on the map.
The map scale is $1:4,500,000$.
This means $1 \text{ cm}$ on the map represents $4,500,000 \text{ cm}$ in reality.
Convert centimeters to kilometers:
$4,500,000 \text{ cm} = 45,000 \text{ m} = 45 \text{ km}$.
So, $1 \text{ cm}$ on the map represents $45 \text{ km}$ on the ground.

Step 2: Measure the straight-line distance between Vryheid and Underberg on the map.
By measuring the map (estimation), the straight-line distance between Vryheid and Underberg is approximately $7.2 \text{ cm}$.

Step 3: Calculate the actual distance.

$$\text{Actual distance} = \text{Map distance} \times \text{Scale factor}$$ $$\text{Actual distance} = 7.2 \text{ cm} \times 45 \frac{\text{km}}{\text{cm}}$$ $$$$