GSEB Class 9 Maths Solutions Chapter 3 Coordinate Geometry Exercise 3.1

Question 1. How will you describe a table lamp on your study table to another person?
Answer: Imagine your study table as a flat surface. Let's label the corners ABCD. We can choose two sides that meet, like AD and DC, to be our x-axis and y-axis. If we place a lamp at a point L, its straight-line distance from the side AB (which is parallel to the y-axis) is 20 cm. This distance becomes the lamp's x-coordinate, also known as the abscissa. Its straight-line distance from the side AD (which is the x-axis) is 15 cm. This distance is the lamp's y-coordinate, also called the ordinate. So, the location or coordinates of the lamp L on the table would be (20, 15).
In simple words: To tell someone where a lamp is on a table, you can use coordinates. Imagine the table's edges as x and y lines. Then, measure how far the lamp is from each edge to get its (x, y) position. For instance, if it's 20 cm from one edge and 15 cm from another, its spot is (20, 15).

Exam Tip: When describing a position using coordinates, always clearly define the origin (0,0) and the positive directions of your x and y axes. Perpendicular distances from the axes determine the coordinates.

Question 2. (Street Plan): A city has two main roads which cross each other at the center of the city. These two roads are along the North-South direction and East-West direction. All the other streets of the city-run parallel to these roads and are 200 m apart. There are 5 streets in each direction. Using 1 cm = 200 m, draw a model of the city on your notebook. Represent the roads! streets by single lines. There are many cross-streets in your model. A particular cross-street is made by two streets, one running in North-South direction and another in the East-West direction. Each cross street is referred to in the following manner: If the second street running in the North-South direction and 5th in the East-West direction meet at some crossing, then we will call this cross-street (2, 5). Using this convention, find:
(i) how many cross-streets can be referred to as (4, 3)
(ii) how many cross-streets can be referred to as (3. 4).
Answer: To create a model of the city, we can draw a coordinate grid. Let the North-South roads be the Y-axis and the East-West roads be the X-axis. Since there are 5 streets in each direction, we'll label them 1 to 5. Each cross-street is where a North-South street and an East-West street meet. Using the given convention, where the first number is the North-South street and the second is the East-West street:
(i) Only one cross-street can be referred to as (4, 3). This is because the 4th North-South street and the 3rd East-West street intersect at a single, unique point.
(ii) Similarly, only one cross-street can be referred to as (3, 4). This happens where the 3rd North-South street and the 4th East-West street cross.
The diagram shows both these unique cross-streets plotted on the grid.
In simple words: When you draw a map of the city streets on a grid, each specific street crossing has its own unique address. So, there is only one place on the map that can be called (4, 3), and only one place that can be called (3, 4).

Exam Tip: In a coordinate system, each ordered pair (x, y) corresponds to exactly one point. This means that a specific location or intersection will always have a unique set of coordinates.