(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 $5^{th}$ 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 $(3, 4).$
$(i)$ how many cross-streets can be referred to as $(4, 3).$
$(ii)$ how many cross-streets can be referred to as $(3, 4).$
(A) Based on the convention provided,the first number represents the street running in the North-South direction,and the second number represents the street running in the East-West direction.
$(i)$ The cross-street $(4, 3)$ is formed by the intersection of the $4^{th}$ North-South street and the $3^{rd}$ East-West street. Since there is only one such intersection point,there is only $1$ cross-street that can be referred to as $(4, 3).$
$(ii)$ The cross-street $(3, 4)$ is formed by the intersection of the $3^{rd}$ North-South street and the $4^{th}$ East-West street. Similarly,there is only $1$ cross-street that can be referred to as $(3, 4).$
$(i)$ The cross-street $(4, 3)$ is formed by the intersection of the $4^{th}$ North-South street and the $3^{rd}$ East-West street. Since there is only one such intersection point,there is only $1$ cross-street that can be referred to as $(4, 3).$
$(ii)$ The cross-street $(3, 4)$ is formed by the intersection of the $3^{rd}$ North-South street and the $4^{th}$ East-West street. Similarly,there is only $1$ cross-street that can be referred to as $(3, 4).$
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In which quadrant or on which axis do each of the points $(-2, 4)$,$(3, -1)$,$(-1, 0)$,$(1, 2)$ and $(-3, -5)$ lie? Verify your answer by locating them on the Cartesian plane.
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$(iii)$ The $x$-coordinate and the $y$-coordinate of the point $L$ are ......... and ......... respectively. Hence,the coordinates of $L$ are (.........,.........)
$(iv)$ The $x$-coordinate and the $y$-coordinate of the point $S$ are ......... and ......... respectively. Hence,the coordinates of $S$ are (.........,.........)
$(i)$ The abscissa and the ordinate of the point $B$ are ......... and ......... respectively. Hence,the coordinates of $B$ are (.........,.........)
$(ii)$ The $x$-coordinate and the $y$-coordinate of the point $M$ are ......... and ......... respectively. Hence,the coordinates of $M$ are (.........,.........)
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$(i)$ The coordinates of $B$.
$(ii)$ The coordinates of $C$.
$(iii)$ The point identified by the coordinates $(-3, -5)$.
$(iv)$ The point identified by the coordinates $(2, -4)$.
$(v)$ The abscissa of the point $D$.
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$(vii)$ The coordinates of the point $L$.
$(viii)$ The coordinates of the point $M$.
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$(ii)$ The coordinates of $C$.
$(iii)$ The point identified by the coordinates $(-3, -5)$.
$(iv)$ The point identified by the coordinates $(2, -4)$.
$(v)$ The abscissa of the point $D$.
$(vi)$ The ordinate of the point $H$.
$(vii)$ The coordinates of the point $L$.
$(viii)$ The coordinates of the point $M$.
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