 Hello and welcome to this session. Let us understand the following problem today. Find the equation of the line joining 3, 1 and 9, 3 using determinants. Now let us write the solution. Let p be a point with vertices x, y be any point on a straight line joining a 3, 1 and b 9, 3. Now let us see the figure. This is the line a b, a with vertices 3, 1, b with 9, 3 and we have assumed a point with vertices x, y. Now it is clear from the figure that a p b are collinear, therefore it implies a, p, b are collinear which implies area of triangle a, p, b is equal to 0 which implies half into 3, 1, 1, x, y, 1, 9, 3, 1 is equal to 0 which implies 3, 1, 1, x, y, 1, 9, 3, 1 is equal to 0 which implies 3 into y minus 3 minus 1 into x minus 9 plus 1 into 3x minus 9y is equal to 0 which implies 3y minus 9 minus x plus 9 plus 3x minus 9y is equal to 0 which implies this gets cancelled so combining the right terms we get minus x plus 3x we get 2x 3y minus 9y we get minus 6y which is equal to 0 which implies x minus 3y is equal to 0 hence our required equation is x minus 3y is equal to 0 I hope you understood the problem bye and have a nice day