How will you describe the position of a table lamp on your study table to another person ?

(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 $1\,cm = 200 \,m$, 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 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 $(3,\, 4).$

Locate the points $(5, \,0)$, $(0,\, 5)$, $(2,\,5)$, $(5,\, 2)$, $(-\,3, \,5)$, $(-\,3, \,-\,5)$, $(5,\, -\,3)$ and $(6,\, 1)$ in the Cartesian plane.

Write the coordinates of the points marked on the axes in Fig.

Plot the points $(x,\, y)$ given in the following table on the plane, choosing suitable units of distance on the axes.