 Hello and welcome to the session. I am Asha and I am going to help you with the following question that says, the perpendicular from the origin to a line meets it at the point minus 2, 9, find the equation of the line. Let us now start with the solution and firstly just interpret the given question in the form of a figure. It denotes O having code in its 0, 0. Now let this point denotes minus 2, 9. Now the line passes through this point. Suppose this is the line, let this line be denoted by P2. Now a perpendicular is drawn from the origin to this line. Suppose this is the perpendicular drawn. Let us denote this point by N. So now we will try to find the slope of line P2. For that we will first find the slope of line NO. Now the coordinates of N is 2, 9 and coordinates of O are 0, 0. So slope is equal to 0 minus 9 upon 0 minus of minus 2. So we have minus 9 upon 2. This is the slope of line NO. Now slope of line PQ which is perpendicular to the line NO is given by minus 1 upon minus 9 upon 2. That is 2 upon 9 since if M1 and M2 are the slopes of two perpendicular lines then the product of their slopes is equal to minus 1. And where the slope of this line is minus 9 upon 2, the slope of line PQ will be given by minus 1 upon the slope of line NO. So this comes out equal to 2 upon 9. Now we will find the equation of line passing through the point minus 2, 9 having slope 2 upon 9 is given by y minus 9 is equal to 2 upon 9 into x minus of minus 2. So we have y minus 9 is equal to 2 upon 9 into x plus 2 or it can further be written as 9 by minus 81 is equal to 2x plus 4 or we have 2x minus 9y is equal to minus 81 minus 4 or 2x minus 9y plus 85 is equal to 0. Therefore equation of the required line is 2x minus 9y plus 85 is equal to 0. So this completes the session. Take care and have a good day.