**Coordinate Geometry**

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

**Solution:**

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

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

Measure the perpendicular distance ‘a’cm of P (lamp) from OY. Measure the perpendicular distance ‘b’ cm of P (lamp) from OX.

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 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 the North-South direction and another in the East-West direction. Each cross street is referred to in the following manner: If the 2 ^{nd} street running in the North-South direction and 5^{th} 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:**

(**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.