Home | Mapping the Plane

How is this possible? Let us work out the procedure of locating a particular address. We know the World is divided into countries.

**Mapping the Plane**

How do you write your address ? Here is one.

**Sarakkalvilai
Primary School**

135, Sarakkalvilai,

Sarakkalvilai Housing Board Road,

Keezha Sarakkalvilai,

Nagercoil 629002, Kanyakumari Dist.

Tamil Nadu, India.

Somehow, this information is enough for anyone in
the world from anywhere to locate the school one studied. Just consider there
are crores and crores of buildings on the Earth. But yet, we can use an address
system to locate a particular person’s studied place, however interior it is.

How is this possible? Let us work out the procedure
of locating a particular address. We know the World is divided into countries.
One among them is India. Subsequently India is divided into States. Among these
States we can locate our State Tamilnadu.

Further going deeper, we find our State is divided
into Districts. Districts into taluks, taluks into villages proceeding further
in this way, one could easily locate Sarakkalvilai” among the villages in that
Taluk. Further among the roads in that village, ‘Housing Board Road’ is the
specific road which we are interested to explore. Finally we end up the search
by the locating Government Primary School building bearing the door number 135
to enable us precisely among the buildings in that road.

In New York city of USA, there is an area called Manhattan. The map shows Avenues run in the North – South direction and the Streets run in the East – West direction. So, if you know that the place you are looking for is on 57th street between 9th and 10th Avenues, you can find it immediately on the map. Similarly it is easy to find a place on 2nd Avenue between 34th and 35th streets. In fact, New Yorkers make it even simpler. From the door number on a street, you can actually calculate which avenues it lies between, and from the door number on an avenue, you can calculate which streets it stands.

All maps do just this for us. They help us in
finding our way and locate a place easily by using information of any landmark
which is nearer to our search to make us understand whether we are near or far,
how far are we, or what is in between etc. We use latitudes (east – west, like
streets in Manhattan) and longitudes (north – south, like avenues in Manhattan)
to pin point places on Earth. It is interesting to see how using numbers in
maps helps us so much.

This idea, of using numbers to map places, comes
from geometry. Mathematicians wanted to build maps of planes, solids and shapes
of all kinds. Why would they want such maps? When we work with a geometric
figure, we want to observe wheather a point lies inside the region or outside
or on the boundary. Given two points on the boundary and a point outside, we
would like to examine which of the two points on the boundary is closer to the
one outside, and how much closer and so on. With solids like cubes, you can imagine
how interesting and complicated such questions can be.

Mathematicians asked such questions and answered
them only to develop their own understanding of circles, polygons and spheres.
But the mathematical tools and techniques were used to find immense
applications in the day to day life. Mapping the world using latitudes and
longitudes would not have been developed at all in 18th century, if the
co-ordinate system had not been developed mathematically in the 17th century.

You already know the map of the real number system
is the number line. It extends infinitely on both directions. In between any
two points, on a number line, there lies infinite number of points. We are now
going to build a map of the plane so that we can discuss about the points on
the plane, of the distance between the points etc. We can then draw on the
plane all the geometrical shapes we have discussed so far, precisely.

Arithmetic introduced us to the world of numbers
and operations on them. Algebra taught us how to work with unknown values and
find them using equations. Geometry taught us to describe shapes by their
properties. Co-ordinate geometry will teach us how to use numbers and algebraic
equations for studying geometry and beautiful integration of many techniques in
one place. In a way, that is also great fun as an activity. Can’t wait ? Let us
plunge in.

Tags : Coordinate Geometry | Mathematics , 9th EM Mathematics : Coordinate Geometry

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9th EM Mathematics : Coordinate Geometry : Mapping the Plane | Coordinate Geometry | Mathematics

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