Question 14 - End-of-Chapter Exercises - Chapter 1 Class 9 - Orienting Yourself: The Use of Coordinates (Ganita

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Question 14 (a) A city has two main roads which cross each other at the centre of the city. These two roads are along the North–South (N–S) direction and East–West (E–W) direction. All the other streets of the city run parallel to these roads and are 200 m apart. There are 10 streets in each direction. (i) Using 1 cm = 200 m, draw a model of the city in your notebook. Represent the roads/streets by single lines. (ii) There are street intersections in the model. Each street intersection is formed by two streets — one running in the N–S direction and another in the E–W direction. Each street intersection is referred to in the following manner: If the second street running in the N–S direction and 5th street in the E–W direction meet at some crossing, then we call this street intersection (2, 5). Using this convention, find: how many street intersections can be referred to as (4, 3). (b) how many street intersections can be referred to as (3, 4). Let’s first draw the streets in North-South and East-West Direction The grids form a graph like in coordinate geometry In coordinate geometry, the numbers (x, y) represents one specific, unique point in a 2-D plane. Now, answering our questions (a) How many street intersections can be referred to as (4, 3)? Exactly 1 This is the intersection of the 4th N-S street and the 3rd E-W street only happens at one specific spot. (b) How many street intersections can be referred to as (3, 4)? Exactly 1 This is the intersection of the 3rd N-S street and the 4th E-W street only happens at one specific spot. Notice that this is a completely different location than $(4, 3)$.