## Chapter 3 Coordinate Geometry Exercise 3.1

Question 1: How will you describe the position of a table lamp on your study table to another person?

Answer:

1. To describe the position of a table lamp placed on the table, let us consider the table lamp as T and the table as a plane.

2. Now choose two perpendicular edges of the table as the axes OX and OY.

3. Measure the perpendicular distance, ‘a’ cm of T (table lamp) from OY. Measure the perpendicular distance, ‘b’ cm of T (table lamp) from OX.

4. Thus, the position of the table lamp P is described by the ordered pair (a, b).

Question 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 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).

Answer:

i) A unique cross street as shown by the point A(4, 3).

ii) A unique cross street as shown by the point B(3,4).

The two cross streets are uniquely found because of the two reference lines we have used for locating them.

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