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, we can consider the flat top surface of the study table as a 2D plane (similar to a Cartesian plane). Let us follow these steps:

1. Choose two perpendicular edges of the table as our axes: let the shorter edge be the Y-axis and the longer edge be the X-axis.
2. Measure the distance of the lamp from both edges. For example, let the distance of the lamp from the shorter edge be 25 cm, and its distance from the longer edge be 30 cm.
3. Using this reference, we can write the position of the lamp as coordinates: (25, 30) or (30, 25), depending on which edge we consider as the starting axis.

Thus, any unique position on a flat table can be represented using a pair of numerical coordinates.

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 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. 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:

By plotting the streets on a grid where the horizontal axis represents the East-West streets and the vertical axis represents the North-South streets, we get clear intersection points:

• (i) Only one unique cross-street can be referred to as (4, 3) because there is exactly one intersection point where the 4th North-South street meets the 3rd East-West street.
• (ii) Only one unique cross-street can be referred to as (3, 4) because there is exactly one intersection point where the 3rd North-South street meets the 4th East-West street.