 Hello and welcome to the session. Let us solve the following question which says the vertices of triangle P q r are P 2, 1 q minus 2, 3 and r is 4, 5. Find equation of the median through the vertex r. So first let us learn some simple ideas with the help of which we will solve the given problem. Suppose we have two points P and q's coordinates are x1, y1 and q is x2, y2. Now the midpoint of these two points P and q is given by x1 plus x2 upon 2 and y1 plus y2 upon 2. So this is the first idea and second is equation of line which passes through P and q is given by minus y1 is equal to y2 minus y1 upon x2 minus x1 into x minus x1. With the help of these ideas we are going to solve the above problem. So this is our key idea. Now start with the solution and firstly let us interpret the given question in the form of a graph figure. Suppose this is triangle P q r, point P is given by 2, 1, q is minus 2, 3 and r is 4, 5. Now we have to find the equation of the median through the vertex r. So suppose rx is the median. So x is the midpoint of line P q. So the coordinates of x is given by the midpoint formula by a key idea that is 2 plus or minus 2 upon 2 comma 1 plus 3 upon 2. Let us get 0 comma 2. So the coordinates of point x are 0 and 2. Now we have to find the equation of line which is the median of this formula. We will find the equation of the line. So here we have x1 is equal to 4, y1 is equal to 5, x2 is equal to 0 and y2 is equal to 2 and thus equation of the line is given by y minus y1 that is 5 is equal to y2 minus 5 and upon x2 minus x1, 2 minus 5 upon 0 minus 4 into x minus x1. So we have x minus 4 or we have y minus 5 is equal to minus 3 upon minus 4 into x minus 4 or we have 4 times of y minus 5 is equal to 3 times of x minus 4 or we have 4 y minus 20 is equal to 3 x minus 12 or 3 x minus 4 y minus 12 plus 20 is equal to 0 or 3 x minus 4 y plus 8 is equal to 0. Thus equation of the line passing through the points r and x is given by 3 x minus 4 y plus 8 is equal to 0 which is the median through the vertex r. So this is our answer. Hope you have understood it. Take care and have a good day.