Eduprobe
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 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 conversion, 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:
Given (2,5) means the intersection of 2nd street from North to South and 5th street from East to West. The figures represent a 2D 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 (i) Only one street can be referred to as (4,3) as we see from the figure as well (ii) Only one street can be referred to as (3,4) as we see from the figure as well.