 Hello and welcome to the session. In this session we will discuss coordinate geometry. We know that position of any object lined in a plane can be represented with the help of two perpendicular lines. This simple idea has far reaching consequences and has given rise to a very important branch of mathematics which is known as coordinate geometry. Now we shall discuss some basic concepts of coordinate geometry. First let's see what is Cartesian system. Cartesian system is basically the system used for describing the position of a point in a plane. When we need to locate the position of an object or a point in a plane, we require two perpendicular lines, one of them is horizontal line and the other is the vertical line. That is we consider these two lines xx dash and yy dash, xx dash is the horizontal line, yy dash as you can see is the vertical line and these two lines are perpendicular to each other. Then we have the plane is called the Cartesian or the coordinate plane and the two perpendicular lines that we take on the plane that is xx dash and yy dash these are called the coordinate axis. This horizontal line xx dash is called the x axis and the vertical line yy dash is called the y axis. Then we have the point of intersection of the axis is called the origin that is this point is the origin and it is represented by the letter O. The coordinate axis divide the plane into four parts called quadrants. The coordinate axis xx dash and yy dash divide this plane into four parts. This is the first quadrant, this is the second quadrant, this is the third quadrant and this is the fourth quadrant. And as you know that quadrant means one fourth part. So the plane consists of the axis and quadrants. We call this plane the coordinate plane or the Cartesian plane or we can also say the xy plane. Now next we see how we write the coordinates of a point. The distance of a point from the y axis is called x coordinate or we also can say fc sub that is it is basically the perpendicular distance of the point from the y axis measured along the x axis. Then distance of a point from x axis is called its y coordinate or we can call it ordinate. It is the perpendicular distance of the point from the x axis measured along the y axis. And when we state the coordinates of a point in the coordinate plane the x coordinate comes first and the y coordinate comes after the x coordinate and they are put in the brackets in this way. We have the positive numbers lie on the direction ox and oy and the negative numbers lie in the directions oy dash and ox dash. That is we say that ox is the positive direction of x axis then oy is the positive direction of y axis. Ox dash is the negative direction of x axis and oy dash is the negative direction of y axis. Next we have coordinates of a point on the x axis is of the form x0 that is in this case the y coordinate is 0 and then coordinates of a point on y axis is of the form 0y that is the x coordinate would be 0 and the coordinates of the origin that is the point o is given by 00 that is this point is 00. That is we say that the origin o has zero distance from both the axis. We have taken xx dash and yy dash the two number lines and we have marked numbers on it the distances are taken from a fixed point and they are marked in equal units positively in one direction and negatively in the other direction and we mark the distances from the fixed point which is the origin. Let's consider this point a in the plane and now we shall find out the coordinates of this point a. As you can see point a is at a distance of positive two units from the y axis and at a distance of positive one unit from the x axis so we have the x coordinate would be its distance from the y axis that is positive two units and the y coordinate would be its distance from the x axis that is one unit so 21 is the coordinate of the point a. The coordinates of a point are of the form plus plus in the first quadrant that is x coordinate would be positive y coordinate would also be positive then the second coordinate it is of the form minus plus that is x coordinate is negative and the y coordinate is positive in the third quadrant it is of the form minus minus that is both the x and the y coordinates are negative fourth quadrant it is of the form plus minus which says x coordinate is positive and y coordinate is negative. Now we shall discuss plotting the point in the plane if its coordinates are given. For this what we do is first we draw the coordinate axis that is x x dash and y y dash and then we choose a unit such that 1 centimeter represents one unit on both the axis. So we have drawn the coordinate axis x x dash and y y dash and we have taken 1 centimeter equal to 1 unit on both the x axis and y axis. Let's consider a point A with coordinates 21. Now we shall plot this point in the plane. This point shows that distance of this point from the y axis along the positive x axis is 2 units and distance of the point from the x axis along the positive y axis is 1 unit. So from the origin O we count 2 units on the positive x axis that is on O x and we mark this point as P. Now from P we move in the positive direction of y axis that is along O y and we move 1 unit that is in this way and we mark this point as A. So this is the point A with coordinates 21. Hence this is the required point A with coordinates 21. Order of x and y is very important in x y so this x y is called the ordered pair that is if we have x is not equal to y then the ordered pair x y is not equal to the ordered pair y x and we have if x is equal to y then ordered pair x y is equal to the ordered pair y x. Let's consider a point P with coordinates 10 and a point Q with coordinates 01. Let's plot these two points P and Q. This is the point P with coordinates 10 and this is the point Q with coordinates 01. So it's evident that the ordered pair x y is not equal to the ordered pair y x. As in this case we have x is not equal to y. So this completes this session. Hope you have understood basic concepts of coordinate geometry.