 Hi friends, I am Purva and today we will discuss the following question. In what ratio does the line x-y-2 is equal to 0, divide the line segment joining 3-1 and 8-9. Let us begin with the solution now. Now, let the required ratio be ks to 1. Now, this is the line x-y-2 is equal to 0 which divides the line segment joining the points a with coordinates 3-1 and b with coordinates 8-9 in the ratio ks to 1. And the point of intersection of the line x-y-2 is equal to 0 and this line segment a-b is p. So, the coordinates of point p which divides the given segment a-b joining the points a with coordinates 3-1 and b with coordinates 8-9 are. Now, the coordinates of the point p which divides the line segment joining the points a with coordinates x-1, y-1 and b with coordinates x-2, y-2 in the ratio ks to 1 are given by k into x-2 plus 1 into x-1 upon k plus 1, k into y-2 plus 1 into y-1 upon k plus 1. So, here the coordinates of this point p which divides the given line segment a-b with coordinates 3-1 and 8-9 in the ratio ks to 1 are given by k into 8 or you can say 8 into k plus 1 into 3 which is equal to 3 upon k plus 1, k into 9 or you can say 9 into k plus 1 into minus 1 which is equal to minus 1 upon k plus 1. Now, since this point p lies on the line x minus y minus 2 is equal to 0, therefore we have coordinates of this point p satisfy the equation of the line x minus y minus 2 is equal to 0. Therefore, we get 8k plus 3 upon k plus 1 minus 9k minus 1 upon k plus 1 minus 2 is equal to 0 or we can write this as 8k plus 3 minus 9k plus 1 minus 2 into k plus 1 is equal to 0. Or you can write this as 8k plus 3 minus 9k plus 1 minus 2k minus 2 is equal to 0 or you can write this as now 8k minus 9k minus 2k is equal to minus 3k and 3 plus 1 minus 2 is equal to plus 2 and this is equal to 0. Or minus 3k is equal to minus 2 or you can say k is equal to 2 upon 3. Therefore, we have the required ratio is 2 upon 3 is to 1 or you can say 2 is to 3. This is our answer. Hope you have understood the solution. Bye and take care.