 Hello and welcome to the session. In this session we discussed the following question which says Determine the ratio in which the line 3x plus y minus 9 equal to 0 divides the segment joining the points 1, 3 and 2, 7. Now we know that if a point, say a point p divides the segment joining the points a with coordinates x1, y1 and b with coordinates x2, y2 in the ratio k is 2, 1 then the coordinates of point p are given by k into x2 plus x1 upon k plus 1 then k into y2 plus y1 upon k plus 1. This is the key idea that we use in this question. Now we move on to the solution. We are given in the question that the line 3x plus y minus 9 equal to 0 divides the segment joining the points 1, 3 and 2, 7. So we suppose that let point a have coordinates 1, 3 and b have coordinates 2, 7 and also we take let the line 3x plus y minus 9 equal to 0 divides the line segment joining the points a with coordinates 1, 3 and b with coordinates 2, 7 in the ratio k is 2, 1 and at point, say point c that is the line 3x plus y minus 9 equal to 0 divides a, b in the ratio k is 2, 1 at point c. So therefore the coordinates of the point c are given by using this key idea it would be given by k into x2 and here x2 would be the x coordinate of the point b that is 2 plus plus x1 that is x-coordinator point A that is 1 upon k plus 1 and the y-coordinator point C is given by k into y2 that is the y-coordinator point B plus y1 that is the y-coordinator point A upon k plus 1 that is we get this is equal to 2k plus 1 over k plus 1 7k plus 3 upon k plus 1 so coordinates of point C are 2k plus 1 upon k plus 1 and 7k plus 3 upon k plus 1. Now the point C lies on the given line that is 3x plus y minus 9 equal to 0 therefore we'll put x equal to 2k plus 1 upon k plus 1 in this equation and y equal to 7k plus 3 upon k plus 1 in this equation that is 3 into 2k plus 1 upon k plus 1 plus 7k plus 3 upon k plus 1 minus 9 is equal to 0. So from here we have 3 into 2k plus 1 plus 7k plus 3 minus 9 into k plus 1 is equal to 0 this further gives us 6k plus 3 plus 7k plus 3 minus 9k minus 9 is equal to 0 from here we get 4k minus 3 is equal to 0 this gives us k is equal to 3 upon 4 so the required ratio would be equal to k is to 1 that is 3 is to 4. So the ratio in which the line 3x plus y minus 9 equal to 0 divides the segment joining the points with coordinates 1, 3 and 2, 7 is 3 is to 4. So with this we complete this session hope you have understood the solution for this question.