 Hello friends, welcome to the session I am Alka, let's discuss coordinate geometry and given question is find the coordinates of the points which divides the joint of minus 1, 7 and 4 minus 3 in the ratio 2 is to 3. So before starting with the solution I would like to tell you the basic idea behind the question, it is section formula. Now suppose there is a given line segment AB with coordinates of AR, X1, Y1 and that of VR, X2, Y2. Now there is a point on the line segment AB that is P which divides the line segment AB in the ratio M1 is to M2. Then coordinates of the point P are given by say X equal to M1 X2 plus M2 X1 upon M1 plus M2 and Y equal to M1 Y2 plus M2 Y1 upon M1 plus M2. So X and Y are the coordinates of the point P which divide the line segment AB in the ratio M1 is to M2. Now let's start with the solution. In the given question we have to find the coordinates of the point P which divides the joint of minus 1, 7 and 4 minus 3 in the ratio 2 is to 3 that is we are given M1 and M2 X2 is to 2 and 3 and coordinates of AR minus 1, 7 and VR 4 minus 3 and we have to find the coordinates of P. So here we can see with the help of a diagram AB as the line segment with coordinates of AR minus 1, 7 and coordinates of VR 4 minus 3 and this is the point P whose coordinates we are supposed to find and the ratio given is 2 is to 3. Now let's just find out by the section formula the coordinates of the point P that is X say X equal to now M1 that is M1 is 2 this is M1 this is M2 now M1 into X2 2 into 4 plus M2 into X1 that is 3 into minus 1 upon M1 plus M2 that is 2 plus 3. So this is equal to 8 minus 3 upon 5 this is equal to 1 therefore X is equal to 1. Now we find the value of Y equal to M1 into Y1 that is 2 into minus 3 plus M2 into Y1 that is 3 into 7 upon M1 plus M2 that is 2 plus 3. So this is equal to minus 6 plus 21 upon 5 this is equal to 15 upon 5 equal to 3 therefore Y equal to 3 therefore the coordinates required point therefore the required answer is 1, 3. So hopefully you understood the solution and enjoyed the session goodbye and take care.