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(Street Plan) : A city has two main roads which cross each other at the center 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 200m apart. There are 5 streets in each direction. Using 1cm=200m, 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).


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Solution

Step 1: Concept used

Let us draw two perpendicular lines as the two main roads of the city that cross each other at the center.

Let us mark them as North-South (represented with N and S) and East-West (represented with E and W).

As given in the question, let us take the scale as 1cm=200m .

Step 2: Determine the cross-streets

Draw five streets parallel to both the main roads (which intersect) to get the given figure below.

The street plan is as shown in the figure:

We can conclude from the given graph that:

(i) From the figure, we can conclude that only one point has the coordinates as (4,3). There is only one cross street, referred to as (4,3).

(ii) From the figure, we can conclude that only one point has the coordinates as (3,4). There is only one cross street, referred to as (3,4).

Hence, (i)There is only one cross street, referred to as (4,3), (ii) There is only one cross street, referred to as (3,4).


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