Given a point on a plane;
given a point on a plane you want to describe how this plane be how this point behaves or
what is the location of this point. Now, if I want to consider this point and I want to describe
the position of the point as of now I cannot say anything more than, this point is slightly
towards the right top of the plane.
Now, if I introduce a horizontal line over here, then I can say the point is in the upper half of
the plane. This gives a slightly better visibility to the point or slightly better description of a
point. Now, if I consider a real number system associated with this line then I can say the
point lies in 0 to 5, if I plot two perpendicular lines between 0 to 5 then I will get this point.
This is much better. Now, these perpendicular lines can also be replaced with one
perpendicular line which is this which has a real number system associated with it. Now,
when a real number system is associated with this point, then what you can actually see is if I
can consider this, this particular structure or this particular square which is enclosed within 5
on the vertical line and 5 on the horizontal line; I am giving a much better description of a
point.
Then I can enhance this further by putting up the grid lines. These grid lines now typically in
this case locate the exact location of the point. So, what is the exact location of the point over
here? If you look at this exact location of the point is on the horizontal line if you travel 3
units in one direction, horizontal direction and 4 units in the vertical direction then you will
reach this point.
So, I can also name this point as in the horizontal direction I have to travel 3 units and in the
vertical direction I have to travel 4 units. So, I can name this point as 3 comma 4 that will be
a precise description of this point. So, in turn what we have seen just now is a reference
system through which we are able to specify the location of a point in a specific manner. Let
us analyze this reference system that we have introduced.
Now, in horizontal direction I have to travel 3 units and in vertical direction I have to travel 4
units; that means, I am actually specifying the coordinates in X direction and coordinates in
vertical direction. So, in particular these horizontal directions and vertical directions are
called X axis and Y axis respectively.
So, if you look at this horizontal direction, you can see the vertical line cuts the horizontal
line into two parts; positive part of X axis and negative part of X axis. Similarly, the vertical
line is cut by the horizontal line into two parts. On the upper side we have a positive part of Y
axis and on the lower side we have a negative part of Y axis.
So, this is a typical structure which is called coordinate plane ok. Now, let us come to the
nomenclature of this particular coordinate plane. As I mentioned if I am travelling 3 units in
horizontal direction; I will call that as X coordinate and if I am travelling 4 units in vertical
direction, I will call that as Y coordinate. Hence, the name coordinates.
These two lines X axis and Y axis meet each other at a 90 degrees angle; that means, both the
lines are perpendicular to each other. Therefore, the name rectangular; recta means right in
Latin so, rectangular means 90 degrees coordinate system; that means, a rectangular
coordinate system. So, let us revise what we have studied just now in words.
The horizontal line is called X axis, it allows you to move from left to right. The vertical line
is called Y axis which allows the movement up and down, then there comes a point of
intersection of these two axes which is called origin. The point of intersection of these two
axes is called origin and if you look at the coordinates of these, then any point on this
particular plane can be denoted by a ordered pair (x, y).
You can see one blue point is also popping up now. Now, how to describe a point using a
coordinate plane? So, for example, given a point (3, 4) how will I locate this point? So, if you
look at this (3, 4), we have already seen how to locate it. We have travelled 3 units in
horizontal direction and 4 units in vertical direction therefore, (3, 4).
Now, suppose you are given another point which is (-5, 2), then this x coordinate
corresponding x coordinate is negative; that means, I have to go to the left of the vertical line.
That means, I have to travel here a 5 units distance which is – 5 and on the positive side of Y
axis I have to travel that is up upper up upper half divided by X axis I have to travel 2 units
which will give me the point (-5 ,2).
So, this is how we can uniquely describe points using coordinate plane. Now, when I was
when we were studying these two points (3, 4) and (-5, 2), you can easily see with respect to
this coordinate axes you can have 4 parts of the coordinate plane.