 Hello and welcome to the session, I am Asha and I am going to help you with the following question that says a line perpendicular to the line segment joining the points 1, 0 and 2, 3 divides it in the ratio 1 is to n, find the equation of the line. First let us learn some simple facts which we shall be using in this problem to solve it. Suppose we have two points p and q and to find the slope of the line joining the points p and q it is formula is y2 minus y1 upon x2 minus x1. Next is suppose this is the line pq, coordinates of pn, x1, y1 and coordinates of q are x2, y2. Suppose a line intersects the line pq at the point r in the ratio of m is to n then to find the coordinates of r a formula is n times of x1 plus m times of x2 upon m plus n comma n times of y1 plus m times of y2 upon n plus n. And the third is equation of the line x1, y1 having slope m is given by y minus y1 is equal to m times of x minus x1. So, this is the equation of the line which passes through a given point x1, y1 and xy is any general point on the line. So, these are some facts which we shall be using in this problem. So, this is our key idea. Let us see how we shall proceed on with the solution. We have given in the question that the line perpendicular to the line segment joining the points 1, 0 and 2, 3 divides it in the ratio 1 is to n. So, let the three line segment rejoin the point pq and 2, 3. And let us denote the point 1, 0 by p and 2, 3 by q and the line divides the line pq in the ratio 1 is to n. Let the point of intersection of these two lines be denoted by r and this line be denoted by xy. So, we have to find the equation of line xy. So, for that first we will find the slope of line xy and then we will find the coordinates of point r and then with the help of the formula for equation of a line we will find the equation of the required line. So, firstly let us find the slope of line where p have coordinates 1, 0 and q has coordinates 2, 3. So, this by a key idea is equal to 2 minus 0 upon 2 minus 1 which is equal to 3. Therefore, slope of line cd is equal to minus 1 upon 3 since two lines are perpendicular to each other having slopes m1 and m2 and the product of their slopes is equal to minus 1. So, let the slope of line p and q be denoted by m1. So, m1 is equal to 3 and we have to find the slope of line cd let us denoted by m2. So, m2 will be equal to minus 1 upon m1 and m1 is 3. So, we have minus 1 upon 3 fine. So, this is the slope of line cd. Therefore, slope of line xy is minus 1 upon 3. Now, let us find the coordinates of r with the help of section formula. So, we have 1 into 2 plus n into 1 upon n plus 1 and 1 into 3 plus n into 0 upon n plus 1. This is further equal to 2 plus n upon n plus 1 comma 3 upon n plus 1. Therefore, coordinates of point r are 2 plus n upon n plus 1 comma 3 upon n plus 1. Now, let us find the equation of the line passing through the point r minus 1 upon 3. So, this is given by y minus 3 upon n plus 1 is equal to minus 1 upon 3 into x minus 2 plus n upon n plus 1 or it can further be written as n plus 1 into y minus 3 on cross multiplying taking 3 on the left hand side and on the right hand side we have minus n plus 1 into x minus 2 plus n upon n plus 1 or we further have 3 times of n plus 1 into y minus 9 is equal to minus n plus 1 inside the bracket taking n plus 1 LCM we have n plus 1 into x minus 2 plus n or we further have 3 times of n plus 1 into y minus 9 is equal to minus of n plus 1 cancels out with n plus 1 and we have n plus 1 into x minus minus plus 2 plus n or we further have n plus 1 into x plus 3 times of n plus 1 into y is equal to n plus 2 plus 9 or n plus 1 into x plus 3 times of n plus 1 into y is equal to n plus 11. Therefore, equation of the line satisfying the given conditions is n plus 1 into x plus 3 times of n plus 1 into y is equal to n plus 11 this completes the session take care and have a good day.