Review the key concepts, formulae, and examples before starting your quiz.
🔑Concepts
The Role of Scale: Since we cannot draw the actual size of cities or roads on paper, maps are drawn using a 'Scale'. A scale tells us the relationship between the distance on the map and the real distance on the ground. For example, if the scale is , then a line on the map represents a real distance of . Visually, this is often shown as a small ruler-like bar at the bottom of a map.
Directions and Orientation: Maps are usually oriented with North at the top. Once you know North, you can find the other cardinal directions: South is opposite to North (bottom), East is to the right, and West is to the left. Visually, maps include a 'Compass Rose' which is a star-like symbol indicating these four directions.
Bird's Eye View: Maps are drawn from a top-down perspective, also known as a 'Bird's Eye View'. This means you only see the tops of objects. For example, a car from the top looks like a rectangle, and a tree looks like a green circle. This perspective helps in showing the layout of a large area clearly.
Landmarks and Symbols: Landmarks are important places like hospitals, parks, or monuments used to give directions. Instead of drawing realistic pictures, maps use simple symbols. For example, a blue line usually represents a river, a small red 'H' inside a square might represent a hospital, and a black dotted line represents a railway track.
Grid Squares and Localization: To find a specific point easily, maps are often divided into a grid of identical squares. Each square can be identified by a column (usually letters like A, B, C) and a row (usually numbers like 1, 2, 3). For instance, a park located in 'Square B2' is found where column B and row 2 intersect.
Enlarging and Reducing Maps: When a map is redrawn from a smaller grid (like squares) to a larger grid (like squares), the picture becomes bigger, but its shape remains identical. Even though the picture looks bigger, the actual distance it represents on the ground remains the same unless the scale value is also changed.
Measuring Curved Paths: Not all roads are straight. To measure a curved road on a map, we can use a piece of thread. We place the thread along the curve of the road on the map, then straighten the thread and measure its length against a ruler to find the map distance.
📐Formulae
💡Examples
Problem 1:
On a map of India, the distance between Delhi and Jaipur is . If the scale of the map is , find the actual distance between the two cities.
Solution:
Step 1: Identify the given values. Map Distance = and Scale = . Step 2: Use the formula: . Step 3: Multiply: . Step 4: The actual distance is .
Explanation:
We multiply the measured distance on the map by the real-world value assigned to each centimeter in the scale to find the total real distance.
Problem 2:
A square park has an area of on a map drawn with grid squares. If the map is redrawn on a grid, what will be the new area of the park on the paper?
Solution:
Step 1: On a grid, an area of means the square has sides of (since ). Step 2: On a grid, every length is doubled. So, the side of the park becomes . Step 3: Calculate the new area: .
Explanation:
When the grid size is doubled, the side lengths of any shape drawn on it also double, which results in the area becoming four times larger ().