 Hello friends, welcome to the session. I am Alka. Let's discuss the given question. Find the ratio in which the line segment joining A and B is divided by the x-axis. Also find the coordinates of the point of division. Now let's start with the solution. Say there is a given line segment AB with coordinates of AR, X1, Y1 and coordinates of PR, X2, Y2. There is a point P which divides the line segment in the ratio of K is to 1 and the coordinates of PR, X and Y. Now by the section formula the coordinates of PR given by K into X2 plus 1 into X1 upon K plus 1 and K into Y2 plus 1 into Y1 upon K plus 1. So these are the coordinates of P. Now according to the question we see that coordinates of the point AR 1 and minus 5, coordinates of the point PR minus 4 and 5 and coordinates of the P we have to find. So they are X and Y. Now we can say that coordinates of point P. Now we will substitute the value of X1, X2, Y1, Y2 from the given question. So this we get K into X2 is minus 4 plus 1 into X1 is 1 upon K plus 1. This is the X coordinate and Y coordinate is K into Y2 that is 5 plus 1 into Y1 that is minus 5 upon K plus 1. So these are the coordinates of the point P which divides the line segment AB in the ratio K is to 1. Now we are given in the question that this point lies on the X axis lies on X axis. So this implies that coordinate of Y is 0. So therefore we can say that 5K minus 5 upon K plus 1 equal to 0. This implies 5K minus 5 equal to 0. This implies K equal to 1. Therefore the ratio will be 1 is to 1. Now we will substitute the value of K equal to 1 in the coordinates of P. We get substituting K equal to 1 in the coordinates of P. We get substituting K equal to 1 in the coordinates of P. We get minus 4 plus 1 upon 1 plus 1 and 5 minus 5 upon 1 plus 1. So we get the coordinates of P is minus 3 upon 2 and 0. So minus 3 upon 2 and 0 are the coordinates of the point P. Therefore the ratio in which the P divides the line segment is 1 is to 1 and the coordinates of quantum division are minus 3 upon 2 and 0. So we can say that the required answer is 1 is to 1 and minus 3 upon 2 and 0. Hope you understood the solution and enjoyed the session. Goodbye and take care.