(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).
o solve the problem, we need to first understand the setup of the streets in the city. The city has two main roads running in the North-South direction and East-West direction, and additional streets running parallel to these two main roads. Each street is 200 m apart, and we're using the scale where 1 cm = 200 m.
The numbering convention for the cross-streets is given as follows:
The first number in the pair (e.g., (4, 3)) refers to the street running in the North-South direction.
The second number refers to the street running in the East-West direction.
There are 5 streets in each direction.
We are given that all streets are 200 m apart, and there are 5 streets in both the North-South and East-West directions. To model this, we can draw a grid with streets placed 1 cm apart, since 1 cm represents 200 m.
For the North-South direction, we will have 5 streets: 1st, 2nd, 3rd, 4th, and 5th. These streets will be represented as vertical lines on the model.
For the East-West direction, we will also have 5 streets: 1st, 2nd, 3rd, 4th, and 5th. These will be represented as horizontal lines on the model.
At each intersection of a vertical and a horizontal line, we will have a cross-street. Each intersection can be referred to by a pair (i, j), where 'i' represents the street number in the North-South direction, and 'j' represents the street number in the East-West direction.
The cross-street (4, 3) refers to the intersection of:
The 4th street in the North-South direction.
The 3rd street in the East-West direction.
There is only 1 cross-street that meets these criteria, which is the intersection of the 4th North-South street and the 3rd East-West street. So, the answer is 1 cross-street.
Similarly, the cross-street (3, 4) refers to the intersection of:
The 3rd street in the North-South direction.
The 4th street in the East-West direction.
There is only 1 cross-street that meets these criteria, which is the intersection of the 3rd North-South street and the 4th East-West street. So, the answer is 1 cross-street.
(i) The number of cross-streets that can be referred to as (4, 3) is 1.
(ii) The number of cross-streets that can be referred to as (3, 4) is 1.