 Hello friends, welcome to the session. I am Malka. Let's discuss the given question. If A and B are minus 2, minus 2 and 2 minus 4 respectively, find the coordinates of P such that AP equal to 3 upon 7 AB and P lies on the line segment AB. So let's discuss the basic idea behind the question. That is, say if there is a given line segment AB with coordinates of AS X1, Y1 and coordinates of PS X2, Y2 and there is a point P which divides the line segment in the ratio of M1, M2 and the coordinates of P are X and Y. Then coordinates of P are given by M1 into X2 plus M2 X1 upon M1 plus M2 and M1 by 2 plus M2 Y1 upon M1 plus M2. These are the coordinates of the point P which divide the line segment AB in the ratio of M1, M2. Now our problem is based on the section formula. So this is called as section formula. Now let's begin with the solution. We have given in the question the coordinates of the point A and B, coordinates of AR minus 2 and minus 2 and coordinates of VR 2 and minus 4 and we have to find the coordinates of the point P. We are given that AP equal to 3 upon 7 AB. So this is equal or we can say that AP upon AB equal to 3 upon 7. This implies AP is 2 AB equal to 3 is 2 7. Therefore we can say that AP is 2 PB equal to 3 is 2 4. As we can see from the figure that when AP is 3 and AB is 7 then PB will be 4. So now since we have to find the coordinates of the point P and we are given with the ratio of AP is 2 PB as 3 is 2 4. Therefore coordinates point P by section formula and having the coordinates of A and B and the ratio is 3 is 2 4. So M1, M2 is 3 and 4. Now we will use the section formula M1, M1 is 3 and M2 is 4. M1 into X2 that is 2 plus M2 that is 4 into X1 that is minus 2 upon M1 plus M2 M1 into Y2 that is minus 4 plus M2 into Y1 that is minus 2 upon M1 plus M2. So this is equal to 6 minus 8 upon 7 and minus 12 minus 8 upon 7. So this is equal to minus 2 upon 7 and minus 20 upon 7. So the coordinates of the point PR minus 2 upon 7 and minus 20 upon 7. Therefore the coordinates of the point PR minus 2 upon 7 and minus 20 upon 7. So hope you understood the solution and enjoyed the session. Goodbye and take care.