 Hello and welcome to the session. Let us discuss the following question. Question says, find the ratio in which the line segment joining the points minus 3,10 and 6 minus 8 is divided by minus 1,6. First of all let us understand that if we are given a line segment AB where coordinates of AR, X1, Y1 and coordinates of BR, X2, Y2 and P divides the line segment AB internally in the ratio K is to 1, then coordinates of P will be KX2 plus X1 upon K plus 1, KY2 plus Y1 upon K plus 1. This is the key idea to solve the given question. Let us now start with the solution. Let us assume that point minus 1,6 divides the line segment joining the points minus 3,10 and 6 minus 8 in the ratio K is to 1. Here we can see this is a line joining points minus 3,10 and 6 minus 8 and minus 1,6 is a point which divides this line in the ratio K is to 1. Now let us assume that coordinates of this point are X1, Y1 and coordinates of this point are X2, Y2. Rarely we can see X1 is equal to minus 3, Y1 is equal to 10, X2 is equal to 6, Y2 is equal to minus 8. Now using key idea we get coordinates of this point is equal to K multiplied by X2 we know X2 is equal to 6, so we can write 6 multiplied by K plus X1, X1 is equal to minus 3, so plus minus 3 upon K plus 1. Now K multiplied by Y2, Y2 is equal to minus 8 plus Y1, Y1 is equal to 10 upon K plus 1. Now we know coordinates on left hand side and coordinates on right hand side will be equal only when this expression is equal to minus 1 and this expression is equal to 6. So we can write this implies 6 K minus 3 upon K plus 1 is equal to minus 1, we know this expression can be written as 6 K minus 3 upon K plus 1. Now simply find we get 6 K minus 3 is equal to minus K minus 1 multiplying both the sides by K plus 1 we get this expression. Now adding K on both sides we get 7 K minus 3 is equal to minus 1. Now adding 3 on both the sides we get 7 K is equal to 2. Now dividing both the sides by 7 we get K is equal to 2 upon 7. Now we get ratio K is to 1 is equal to 2 is to 7. So we get the point minus 1 6 divides the line segment joining the points minus 3 10 and 6 minus 8 in the ratio 2 is to 7. We can check this ratio for Y coordinate also. Now let us make a check for Y coordinate also we can write minus 8 K plus 10 upon K plus 1 is equal to 6. Now multiplying both the sides by K plus 1 we get minus 8 K plus 10 is equal to 6 K plus 6. Now transposing light terms we get minus 8 K minus 6 K is equal to 6 minus 10. Now this implies minus 14 K is equal to minus 4 we know minus 8 K minus 6 K is equal to minus 14 K and 6 minus 10 is equal to minus 4. Now dividing both the sides by minus 2 we get 7 K is equal to 2. Now dividing both the sides by 7 we get K is equal to 2 upon 7. Now this implies ratio K is to 1 is equal to 2 is to 7. So this verifies our answer. So our required answer is 2 is to 7. This completes the session. Hope you understood the session. Take care and have a nice day.