 Hello friends, welcome to the session. I am Malka. Let's discuss the given question. It will be the ratio in which the line 2x plus y minus 4 equal to 0 divides the line segment joining the points A with coordinates 2 minus 2 and B with coordinates 3, 7. Now let's start with the solution. In the question we are given a line segment AB with coordinates of A, 2 minus 2 and coordinates of B as 3, 7 and it is given that the line segment AB is divided by another line that is 2x plus y minus 4 equal to 0. We suppose that the line 2x plus y minus 4 equal to 0 divides the line segment AB at the point P and the point P divides the line segment AB in the ratio of K is to 1. Now we all know that to find the coordinate of the point P we use a section formula therefore by section formula which is given by m1x2 plus m2x1 upon m1 plus m2 and m1y2 plus m2y1 upon m1 plus m2. These are the coordinates of the point P. Now since we have assumed that the point P divides the line segment AB in the ratio of K is to 1 therefore AP is to PB is equal to K is to 1. Now by applying section formula we will find the coordinates of the point P that will be here m1 and m2 are K and 1, m1 is K and m2 is 1. Now m1 is K so it will be K into x2 that is 3 plus m2 is 1 into x1 is 2 upon K plus 1. This is the x coordinate now we will find the y coordinate so it is given by m1 that is K into y2 that is 7 plus m2 that is 1 into y1 that is minus 2 upon K plus 1. So these are the coordinates of the point P. This can also be written as 3 K plus 2 upon K plus 1 and 7 K minus 2 upon K plus 1. These are the coordinates of point P. Now since we know that this point P lies on the given line that is 2x point P lies on the line 2x plus y minus 4 equal to 0 then these points the coordinates of the point P must satisfy the given line that is 2 into x. Now we will write the coordinate of the point P 3 K plus 2 upon K plus 1 plus y that is 7 K minus 2 upon K plus 1 minus 4 equal to 0. Now taking LCM and simplifying we get 6 K plus 4 plus 7 K minus 2 minus 4 K minus 4 equal to 0 or 13 K minus 4 K equal to 2 or this can also be written as 9 K equal to 2. This implies K equal to 2 by 9 therefore we can say that ratio is 2 is to 9. Therefore we can say that the ratio in which the line divides the given line segment AB is 2 is to 9. So hope you understood the solution and enjoy the session. Goodbye and take care.