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 $200$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 conversion, find:$\left(i\right)$ How many cross-streets can be referred to as $(4,3)$
$\left(ii\right)$ How many cross-streets can be referred to as $(3,4)$.

Answer 1

Given $(2,5)$ means the intersection of $2^{\text{nd}}$ street from North to South and $5^{\text{th}}$ street from East to West.
The figures represents 2 D plane, in which each pair of perpendicular lines intersect only once,
thus, the two different streets from North to South and East to West intersect only once.
$\left(i\right)$ Only one street can be referred to as $(4,3)$ as we see from the figure as well.
$\left(ii\right)$ Only one street can be referred to as $(3,4)$ as we see from the figure as well.