Using a graphic scale, measure the direct distance between Bloemhof and Lichtenburg on the map and calculate…

Question

Using a graphic scale, measure the direct distance between Bloemhof and Lichtenburg on the map and calculate the actual distance in kilometers and miles.

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Here are the solutions to the questions:

QUESTION TWO

2.1.1

The type of scale used in the map is a graphic scale or bar scale.

2.1.2

To measure the direct distance, you would use a ruler on the map.

First, measure the length of the 80 km segment on the provided bar scale. Let's estimate this to be approximately $35 \text{ mm}$ .
Next, measure the straight-line distance between Bloemhof and Lichtenburg on the map. Let's estimate this to be approximately $45 \text{ mm}$ .

Therefore, the estimated direct distance from Bloemhof to Lichtenburg on the map is $\boxed{\text{45 mm}}$ .

2.1.3

Determine the map scale.
From the bar scale, $35 \text{ mm}$ on the map represents $80 \text{ km}$ in reality.
So, $1 \text{ mm}$ on the map represents $\frac{80}{35} \text{ km}$ .
Calculate the actual distance in km.
Using the estimated map distance of $45 \text{ mm}$ from 2.1.2:
$\text{Actual distance} = 45 \text{ mm} \times \frac{80}{35} \frac{\text{km}}{\text{mm}}$ $\text{Actual distance} = \frac{45 \times 80}{35} \text{ km}$ $\text{Actual distance} = \frac{3600}{35} \text{ km}$ $\text{Actual distance} \approx 102.86 \text{ km}$
The actual distance from Bloemhof to Lichtenburg is approximately $\boxed{\text{102.86 km}}$ .

2.1.4
Convert the actual distance from km to miles.
We know that $1 \text{ mile} \approx 1.60934 \text{ km}$ .
So, $1 \text{ km} \approx \frac{1}{1.60934} \text{ miles}$ .
Using the actual distance from 2.1.3:
$\text{Actual distance in miles} = 102.86 \text{ km} \times \frac{1}{1.60934} \frac{\text{miles}}{\text{km}}$ $\text{Actual distance in miles} \approx 63.91 \text{ miles}$
The actual distance from Bloemhof to Lichtenburg is approximately $\boxed{\text{63.91 miles}}$ .

2.1.5
State the map scale in consistent units.
From the bar scale, $35 \text{ mm}$ on the map represents $80 \text{ km}$ in reality.
Convert $80 \text{ km}$ to millimeters:
$1 \text{ km} = 1000 \text{ m}$
$1 \text{ m} = 1000 \text{ mm}$
So, $1 \text{ km} = 1000 \times 1000 \text{ mm} = 1,000,000 \text{ mm}$ .
Therefore, $80 \text{ km} = 80 \times 1,000,000 \text{ mm} = 80,000,000 \text{ mm}$ .
Express the scale as a ratio.
The scale is $35 \text{ mm} : 80,000,000 \text{ mm}$ .
To get a ratio scale of $1:n$ , divide both sides by 35:
$1 : \frac{80,000,000}{35}$ $1 : 2,285,714.29$
The ratio scale is approximately $\boxed{1:2,285,714}$ .

Using a graphic scale, measure the direct distance between Bloemhof and Lichtenburg on the map and calculate the actual distance in kilometers and miles.

Step-by-step solution

QUESTION TWO

2.1.1

2.1.2

2.1.3

Determine the map scale.

Calculate the actual distance in km.

2.1.4

Convert the actual distance from km to miles.

2.1.5

State the map scale in consistent units.

Express the scale as a ratio.

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