High students, welcome to this section where we deal with Kornet geometry.
Let's get started.
Imagine that you have a piece of paper over here, right?
And there is a dot on the paper.
And you want to describe to somebody where the dot is.
Now, if you tell that person this dot is five centimeters from the bottom.
Is that enough to describe the dot?
No.
Right.
Because you could have a point over here also or a point over here also that satisfies the given condition.
But if you tell the person it's five centimeters from the bottom of the paper and it is 12 centimeter
from the left border of the paper, then you can uniquely identify where the dot is located.
Right.
So that means we need two independent informations for finding the position of the dot right now.
This is the concept behind the Cartesian system, right where we describe the position of a point in
a plane.
Now there is corner geometry, even for three dimensional geometry.
But in this section, we only deal with two dimensional coordinate geometry.
All right.
Now let's try to understand what the Cartesian system is.
Now, over here we have two axis and they are placed perpendicular to one another.
Now, that's why this angle over here is 90 and let them intersect at point all.
And we call this point the origin.
Now, this axis over here is called the x axis.
All right, and this Axe's over here is called the Y-axis.
All right, now I have I put measurements on this in such a way that whatever is on this side is the
positive value for the x axis values, and this side will have the negative values for the X axis.
Similarly, this up over here is the positive Y axis and this is the negative y axis.
All right.
Now let's plot a few points to see how this actually works.
All right, so I have plotted a few points over here, you can see that you have one over here to over
here, three over here, and it keeps going on like this.
Now, over here, the negative axis, you have minus one, minus two, minus three, etc..
Now, remember, the distance between these two will be the same, and that's the same distance over
here as well as over here.
So it's one unit distance, right.
And that same distance is maintained across.
But even here also, you will have one unit distance.
All right, now let's proceed.
Now you can see that we call this x axis and y axis, right?
That axis is the word that we used.
Now, if you take them together, it's called axis.
That's the plural way of writing axis.
Now you can see that these two axis divides the plane.
This is the plane, right?
This is the plane plane surface.
It divided this plane into four parts and we call these parts quadrants.
So therefore, quadrants are one, two, three and four.
You can see that in the first quadrant, anything located in the first quadrant as opposed to x axis
value and the positive y axis value.
Now, soon we will plot points and this will become more clear.
But over here, you can see that X is negative.
But why is positive all here?
Why is negative and X is negative.
And in the fourth quarter you can see that X is positive and Y is negative.
All right.
Now the plane is called also the Cartesian plane or the coordinate plane or the X Y plane and the X
and Y axis are called the coordinate axis.
Let's plot some points and analyze them to understand the x y plane in a better manner.
All right.
Over here we have point B and this is Point Cube.
Now, what is the X coordinate of point B?
You will see that the X coordinate of point B is equal to two.
What is this to these two?
Is this distance that is it's the perpendicular distance from the Y axis measured along the x axis.
Right.
Or to get two point two from y axis, you need to move two units.
Similarly, the Y coordinate of point B will be one unit right now.
The X coordinate is also called the APSA.
And we have seen that the Y coordinate over here is one, right, because you need to move one unit
from the X axis to get to point B, and this over here is also called the ordinate.
All right, now we have checked point B, we have seen what the APSA and Ordinate is now to call point
B or to the point B, we say P to one.
That means this point B is two units from the Y axis or the X coordinate is two and the Y coordinate
is one.
All right.
Now what about point?
Q You will see that point.
Q is three units along this axis, right?
And it is one unit along this axis.
So the X coordinate, four point two is minus three and the Y coordinate is minus one.
Therefore we are right to minus three.
Minus one.
Let's plot some points to solidify our learning so far.
All right.
I have four points over here.
Now, let's start with point A..
Now, over here you can see that the X coordinate of point is minus three, right?
So I need to move three units still here.
Right.
And the Y coordinate is four.
So I need to move four units along this axis.
So that's one, two, three and four.
Now, these two will meet over here and this is point eight and point is minus three.
All right.
Now, what about point B?
The X coordinate is minus two.
So I need to travel down here and the Y coordinate is minus two.
So I need to travel here and they need around over here.
Right.
So this is point B.
Now what about point C?
It has a zero X coordinate for the X coordinated zero at this point.
Right now the Y coordinate is three point five.
So that's one, two, three and three point five will be in between three and four.
Right.
Therefore, point C is over here.
That's zero three point five.
Right.
What about point B?
Point B is six point five zero to the X coordinate is six point five to let me travel six point five
units in this direction.
I reach about here.
Right.
And the Y coordinate is zero to that's over here itself.
Therefore point these over here.
This is six point five zero.