 Hello and welcome to the session. In this session we discuss a question which says that a part write the ordnance in which the following pair lie. First subpart is the audit pair minus 2 5, second subpart the audit pair minus 5 minus 5 and the third subpart is the audit pair 4 minus 3. And in the detail we have to study the graph that is we have to study the following graph in which we have to find out the audit pairs for the different points given in this graph that is for the points P, Q, R, S, T and U. Now before starting the solution of this question we should know some results. And the first result is in the coordinate plane we have four coordinates and here x-axis and y-axis intersect each other at the point O which is the origin and this is the quadrant 1 in which both x and y coordinates are positive and in the second quadrant the x-coordinate is negative whereas the y-coordinate is positive. In the third quadrant the x and y-coordinates are negative that is both the x-y-coordinates are negative, x-coordinate is positive and y-coordinate is negative. Now we can see it graphically also. Now here this is the first quadrant. Now here of origin that is on the x-axis we will have the positive integers like 1, 2, 3, 6 and so on the origin on the y-axis. Again we will have the positive integers as in the first quadrant both x and y-coordinates are positive. Now in the second quadrant it is negative. You can see that the y-coordinates are positive. On the method of origin x-axis we will write the negative integers that is minus 1, minus 2, minus 3, minus 4 and so on. So here in the second quadrant the x-coordinate is negative whereas the y-coordinate is positive. This is the third quadrant and in the third quadrant the x- and y-coordinates are negative that is the x- and y-coordinates those are negative. So here below the origin on the y-axis we will have the negative integers. Here you can see that both the x- and y-coordinates in the third quadrant are negative and finally in the fourth quadrant whereas the y-coordinate is negative. Place the integers on the x-axis and y-axis at equal distances just like we place them on the number line. And the second result is y-coordinate is coordinate. Now these results will work out as a key idea for solving out the given question. And now we start with the solution. In the A part we have to write the quadrant in which part we have the odd pair minus 2. The idea we will check that in which quadrant the x-coordinate is negative and y-coordinate is positive. In the key idea you can see that in the second quadrant the x-coordinate is negative whereas the y-coordinate is positive. So this is the point minus 2 5 which will lie in the second quadrant. The point minus that is the odd pair minus 2 5 lies in the second quadrant. Seconds are part but we have the odd pair minus 5 minus 5 that is here the x-coordinate is minus 5 which is negative and the y-coordinate is again higher which is negative. Let us see from the key idea that in which of the programs both x and y-coordinates are negative. That in the third quadrant both x and y-coordinates are negative. So the point minus 5 minus 5 that is the odd pair minus 5 minus 5 lies in the third quadrant. Therefore we can write that the odd pair minus 5 minus 5 now for the third subpart is given as 4 minus 3. Now here the x and the y-coordinate is minus 3 which is negative. Now let us check in which of the programs the x-coordinate is positive and the y-coordinate is negative. Now here in the fourth quadrant it is positive whereas the y-coordinate is negative. You can see that so we can write that the odd pair that is the point which is represented by the odd pair 4 minus 3 lies in the fourth quadrant which we have to study this graph and we have to name the odd pairs with respect to each point in this graph. Now here lies in the third quadrant so here x and y-coordinates both are. Now the line from x is coming from the point minus 4 so the x-coordinate is minus 2 and the y-coordinate is minus 4 so the odd pair representing the point P is minus that is the x-coordinate is minus 2 and here the y-coordinate is minus 4. Now the point Q lies in the first quadrant which means point x and y-coordinates are positive. Now the line from x is coming from the point 5 and y-coordinate for representing the point Q is how the point U lies in the second quadrant so negative and the y-coordinate is from the point minus 4 and the line from y is coming from the point 3 so the odd pair for representing the point U is minus 4 so the x-coordinate is positive and y-coordinate is negative from the point 3 and from y it is coming from the point minus 5. Here for representing the point R now the point S lies on the x- axis. Now from the clear idea we know that if any point lies on the x- axis then its y-coordinate is 0 the coordinate of the point S is 0 and lies on the x-axis at minus 5 is minus 5 so the odd pair for representing the point S and T lies on the y-axis we know that if any point lies on the y-axis then its x-coordinate is 0 and of the point T is 0 and this point lies on the y-axis of the point T is 0 so we have obtained the ordered pairs with respect to each given point in the graph and this is the solution and that's all for this session. Hope you all have enjoyed this session.