Chapter 3 – Coordinate Geometry
Exercise 3.1 Page: 45
1. How will you describe the position of a table lamp on your study table to another person?
Solution:
To describe the position of the table lamp on the study table, we take two lines, a perpendicular and a horizontal line. Considering the table as a plane (x and y axis) and taking perpendicular lines as the Y axis and horizontal as the X axis, respectively, take one corner of the table as the origin, where both X and Y axes intersect each other. Now, the length of the table is the Y-axis, and the breadth is the X-axis. From the origin, join the line to the table lamp and mark a point. The distances of the point from both the X and Y axes should be calculated and then should be written in terms of coordinates.
The distance of the point from the X-axis and the Y-axis is x and y, respectively, so the table lamp will be in (x, y) coordinates.
Here, (x, y) = (15, 25)
2. (Street Plan): A city has two main roads which cross each other at the centre 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 1cm = 200 m, draw a model of the city in 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 the North-South direction and another in the East-West direction. Each cross street is referred to in the following manner: If the 2nd 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)?
Solution:
- Only one street can be referred to as (4,3) (as clear from the figure).
- Only one street can be referred to as (3,4) (as we see from the figure).