Draw a line scale to show 1 cm represents 100 m . On a map of a scale of \( 1: 1000 \), the distance between two points is 10 How far apart are they on the ground? On a map of a scale of \( 1: 1000000 \), two places are 3 cm apart. How far apart are they on the ground? culate distances between settlements (global and

Let's break down the problem step by step. ### Step 1: Understanding the Scale 1. **Line Scale**: A line scale where 1 cm represents 100 m means that for every 1 cm on the scale, the actual distance on the ground is 100 m. ### Step 2: Calculating Distances on the Ground #### Part A: Map Scale of \( 1: 1000 \) - **Given**: The distance between two points on the map is 10 cm. - **Scale**: \( 1: 1000 \) means that 1 cm on the map represents 1000 cm (or 10 m) on the ground. To find the actual distance on the ground, we can use the formula: \[ \text{Actual Distance} = \text{Map Distance} \times \text{Scale Factor} \] Where the scale factor for \( 1: 1000 \) is 1000. Calculating the actual distance: \[ \text{Actual Distance} = 10 \, \text{cm} \times 1000 = 10000 \, \text{cm} \] Now, converting cm to meters (since 100 cm = 1 m): \[ \text{Actual Distance} = \frac{10000 \, \text{cm}}{100} = 100 \, \text{m} \] #### Part B: Map Scale of \( 1: 1000000 \) - **Given**: The distance between two places on the map is 3 cm. - **Scale**: \( 1: 1000000 \) means that 1 cm on the map represents 1000000 cm (or 10 km) on the ground. Using the same formula: \[ \text{Actual Distance} = \text{Map Distance} \times \text{Scale Factor} \] Where the scale factor for \( 1: 1000000 \) is 1000000. Calculating the actual distance: \[ \text{Actual Distance} = 3 \, \text{cm} \times 1000000 = 3000000 \, \text{cm} \] Now, converting cm to kilometers (since 100000 cm = 1 km): \[ \text{Actual Distance} = \frac{3000000 \, \text{cm}}{100000} = 30 \, \text{km} \] ### Summary of Results - For the map scale of \( 1: 1000 \), the actual distance on the ground is **100 m**. - For the map scale of \( 1: 1000000 \), the actual distance on the ground is **30 km**.