 Hello and welcome to the session the given question says, determine the ratio in which the point P M6 divides the join of A and B also find the value of N. First let us learn the key idea which is the formula called the section formula with the help of which we shall be solving the given problem. Here if we have two points A and B and the point P divides it in the ratio M1 is to M2 then the coordinates of X and Y is given by this formula that is the X coordinate is M1 into X2 plus M2 into X1 divided by M1 plus M2 and the Y coordinate is given by M1 into Y2 plus M2 into Y1 divided by M1 plus M2. So let us now move on to the solution and let P divides the join of AB such that the coordinates of P are M and 6 coordinates of A is 4 minus 4 3 and coordinates of B are 2 and 8. We have to find the value of M and also we have to find the ratio in which the point P divides the join of A and B. Also let the ratio in which P divides the join of ABB K is to 1 so let AP is to PB be equal to K is to 1. Now by the section formula the coordinates of P are given by K into 2 plus 1 into minus 4 divided by K plus 1 and 6 is equal to 8 K plus 3 divided by K plus 1 and this is with the help of section formula on comparing we have 6 equal to 8 K plus 3 divided by K plus 1 this implies that 6 K plus 6 is equal to 8 K plus 3 which further implies that 2 K is equal to 3 or K is equal to 3 divided by 2. Therefore we have AP divided by PB is equal to 3 by 2 divided by 1 or AP is to PB is equal to 3 is to 2. So the ratio in which the point P divides the join of AB is 3 is to 2. Now let us compare the X coordinate this implies that M is equal to 2K minus 4 divided by K plus 1 and now K is 3 divided by 2 so we have M is equal to 2 times of 3 divided by 2 minus 4 whole divided by 3 divided by 2 plus 1 or we have M equal to 3 minus 4 divided by 5 by 2 or this implies M is equal to minus 1 into 2 by 5 which is equal to minus 2 by 5. Hence the answer is the required ratio is 3 is to 2 and the value of M is equal to minus 2 by 5. This completes the session. Bye and take care.