Question

(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 $200\mathrm{m}$ apart. There are $5$ streets in each direction. Using $1\mathrm{cm}=200\mathrm{m}$, 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 ${2}^{\mathrm{nd}}$ street running in the North-South direction and ${5}^{\mathrm{th}}$ 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 $(3,4)$.

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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 $1\mathrm{cm}=200\mathrm{m}$ .

**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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