 Hello and welcome to the session. In this session, we shall study the concept of coordinate plane, ordered pairs, sign of numbers in ordered pairs, their location in coordinate plane and its reflection across one or both axes. First of all, let us discuss the meaning of ordered pair. Now let us consider a relation y is equal to x plus 1. Now where if we put any value of x, then we will get the corresponding value of y. That is, where x is the input, y is the output. Now for x is equal to 0, we get y is equal to, now in this equation we will put x is equal to 0. So we will get y is equal to 0 plus 1 which is equal to 1. Now we take any other value of x, that is for x is equal to 1, we get y is equal to 1 plus 1, that is 2. Now for x is equal to 2, we get y is equal to 2 plus 1, that is put y will be written input, that is y, that is the ordered pair x, y which means we can write values in terms of pairs, the pair put output. Now here input is 0, output is 1. So these values are written as the pair 0, 1 and here it will be the pair 1, x and y, they will have the pair 2. So these points, that is all these points, where the input is the x coordinate is the y coordinate. So we can write as the pair A, B is an ordered pair corresponds to the x coordinate B corresponds to the y coordinate. Now let us discuss the concept of coordinate plane and other pair and we know that every other pair corresponds to the x coordinate corresponds to the y coordinate, these points, that is we can locate these ordered pairs on a graph paper by forming a coordinate plane. Now in a coordinate plane, that is x axis, now for locating the x coordinate, that is A on the x axis, we have to form a coordinate plane on a graph. Now for locating the coordinate plane on the graph, in the first step, we will draw a horizontal line with the sign of arrows on both ends on the graph paper. So here we have drawn a horizontal line with the sign of arrows on both ends on a graph paper, we label this line as, now we will draw a vertical line with the sign of arrows on both ends intersecting the horizontal line perpendicularly in this vertical line with the origin here at this point. The origin, the x and y coordinates are 0, that is the x coordinate is also 0 and y coordinate is also 0 at the origin. Now on both the x and y axis, we will write the integers at a distance of 1 unit on the graph just like a number line. So we have written the integers on both the x and y axis and on the x axis we will write the negative integers on the left of 0 and the positive integers on the right of 0, that is the origin. On the y axis we will write the negative numbers below 0 and the positive numbers above 0 at the same distance here. The distance between the points should be equal. This is the required coordinate plane in which we have both the x and y axis which are intersecting each other at the origin and here you can also see from the graph that the two axis divide the coordinate plane in four regions the coordinates. Here this is called the second quadrant. So we can write that a horizontal number line and a vertical number line per region which are called. Now let us discuss of numbers in ordered pairs. The y coordinates are positive negative for example 1. Now we have enriched x coordinate is negative whereas the y coordinate is positive. For example the ordered pair minus 2, now next is the type 4 that is the ordered pair in which both i coordinates are negative for example ordered pair minus ordered pairs in which the y coordinate is 0 and the other coordinate can be positive or negative. For example the ordered pair 2 0 0 minus. Now let us locate these points on the coordinate plane. Now for locating these points on the coordinate plane we will consider the coordinate plane which we have made previously. Now here in the coordinate plane we have four quadrants. Now we can locate the ordered pairs according to the signs of the numbers in the given ordered pair. Now we can see in the graph that in the quadrant 1 both x and the y coordinates are positive and in the quadrant 2 the x coordinate is negative whereas the y coordinate is positive. In the third coordinate is negative and here the y coordinate is also negative. In the last quadrant make a table for these ordered pairs. Now in this table in the first column we have written the ordered pairs we will find that in which of the quadrants these ordered pairs will line the point which is represented by the ordered pair 2, 3 on the graph. Now for the ordered pair 2 and y coordinate is 3 both of the x and y coordinates are positive. In the first quadrant 2 and 3 which is 9 in the first quadrant lies in the first quadrant. Now let us take the ordered pair 2 minus 1. Now in this case the x coordinate is 2 which is positive and y coordinate is minus 1 which is negative. I in the fourth quadrant the x coordinate is positive and y coordinate is negative. So the ordered pair 2 minus 1 lies in the fourth quadrant. Now let us take the next ordered pair which is minus 2 1. Now here the x coordinate is minus 2 which is negative and y coordinate is 1 which is positive. Now we know that in the second quadrant we had negative and y coordinate positive. So the ordered pair 1 lies in the second quadrant. Take the ordered pair minus 2 minus 3. Now here you can see that the x coordinate is minus 2 which is negative and the y coordinate is minus 3 which is again negative. Now we know that in the third quadrant both x and y coordinates are negative. So the ordered pair minus 2 minus 3 lies in the third quadrant. So the point minus 2 minus 3 lies in the third quadrant. Now the point where the x coordinate is 0 that is the ordered pairs like 0 minus 4 lies the y axis. The y coordinate is 0. For example the ordered pair 2 0 lies these two points on the graph. Now in the ordered pair 2 0 the x from the origin we will move to the right on the x axis and we will reach to this point. The y coordinate is 0 so we will not move and down any units whose coordinates are 2 0 and you can see this point is 0. So this point lies on the x axis. See this is the point whose coordinates are 0 minus 4. The x coordinate of the human point is 0 so this point lies on the y axis. Now let us discuss the reflection of a point across one or both axis. In reflection of the point the image of the point is from the central line or also known as the middle line. Now here is about which we will find the reflection of the point. Now let us take a point A whose coordinates are 2 3 on the graph. So our coordinates both are positive as this point is lying in the first quadrant. Now suppose we take the middle line for the point point A that is A dash will lie in the fourth quadrant since the distance of reflection is same from the central line therefore the numbers will be same only that sign will change according to the quadrant in which the reflection lies. Now here the distance of A from the central line that is x axis and the distance of A there which is the reflection of from the x axis of A are 2 3 and its reflection with the central line as x whose coordinates are 2 minus 3. This reflection of the point A whose coordinates are 2 3 by taking y axis as the central line its reflection point will lie in the second quadrant that is we will obtain a point B whose coordinates are minus 2 3. Therefore the point B is the reflection of the point A across the y axis. We have learnt about the concept of coordinate plane, ordered pairs, sign of numbers in ordered pairs, their location in coordinate plane and its reflection across one or both axis. So this completes our session. We hope you all have enjoyed the session.