Exercise 3.1 Practice
Introduction to Coordinate Geometry
Q1: Position of Lamp
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How will you describe the position of a table lamp on your study table to another person?
To describe the position of the table lamp, we can use the concept of coordinates.
1. Consider the table top as a plane surface and the lamp as a point.
2. Choose two perpendicular edges of the table as axes (say, the longer edge as X-axis and the shorter edge as Y-axis).
3. Measure the distance of the lamp from the longer edge (say, 25 cm).
4. Measure the distance of the lamp from the shorter edge (say, 30 cm).
2. Choose two perpendicular edges of the table as axes (say, the longer edge as X-axis and the shorter edge as Y-axis).
3. Measure the distance of the lamp from the longer edge (say, 25 cm).
4. Measure the distance of the lamp from the shorter edge (say, 30 cm).
We can then describe the position of the lamp as (30, 25) or (25, 30), depending on the order of axes chosen.
By measuring distances from two perpendicular edges (e.g., 30 cm, 25 cm).
Q2: Street Plan
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(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 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 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).
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).
Model Construction:
- Draw two perpendicular lines representing the main roads (N-S and E-W).
- Draw 5 parallel lines to the N-S road and 5 parallel lines to the E-W road.
- Draw two perpendicular lines representing the main roads (N-S and E-W).
- Draw 5 parallel lines to the N-S road and 5 parallel lines to the E-W road.
(i) Cross-street (4, 3):
This refers to the intersection of the 4th street running North-South and the 3rd street running East-West.
Since there is only one 4th N-S street and one 3rd E-W street, they intersect at a unique point.
Thus, there is only one cross-street referred to as (4, 3).
This refers to the intersection of the 4th street running North-South and the 3rd street running East-West.
Since there is only one 4th N-S street and one 3rd E-W street, they intersect at a unique point.
Thus, there is only one cross-street referred to as (4, 3).
(ii) Cross-street (3, 4):
This refers to the intersection of the 3rd street running North-South and the 4th street running East-West.
Similarly, this intersection is unique.
Thus, there is only one cross-street referred to as (3, 4).
This refers to the intersection of the 3rd street running North-South and the 4th street running East-West.
Similarly, this intersection is unique.
Thus, there is only one cross-street referred to as (3, 4).
(i) Only one, (ii) Only one