 Hello and welcome to the session. In this session we discuss the following question that says find the ratio in which the point minus 9, 1 divides to join the points minus 4, 4 and 1 serving. Now consider the two points, so a and b, a has coordinates x1, y1 and b has coordinates x2, y2 and let p be a point with coordinates x, y on a, b and this point p divides a, b and 1 is 2 and 2. So the coordinates of point p are given by x equal to m1 x2 plus m2 x1 this whole over m1 plus m2 and y is equal to m1 y2 plus m2 y1 and this whole over m1 plus m2. This is the key idea that we use for this question. We want the solution now. Now we are supposed to find the ratio in which the point minus 9, 1 divides to join the points minus 4, 4 and 1, 7. We suppose let the required ratio be lambda is to 1. We suppose let the coordinates the point of division be x, y. That is the point of division we point p with coordinates x, y and we suppose that the point p have the coordinates minus 4, 4 and point b have the coordinates 1, 7. So this means that the point p with coordinates x, y the join of a, b, lambda is to 1. In this case we have m1 is lambda, m2 is 1, then x1 is the x coordinate of point a that is minus 4, y1 is the y coordinate of point a that is 4. Then x2 is the x coordinate of point b that is 1 and y2 is the y coordinate of the point b that is 7. Now using this formula to find the coordinates of the point of division we find out x and y. So therefore we have x is equal to m1 x2 that is lambda into 1 that is lambda plus m2 x1 that is 1 into minus 4 which is minus 4 m1 plus m2 that is lambda plus 1. So this is equal to lambda minus 4 over lambda plus 1 that is m8 is equal to m1 y2 that is lambda into 7 is 7 lambda m2 y1 that is 1 into 4 which is 4. This whole point lambda plus 1 that is m1 plus m2. Now in the question we have that the point minus 9, 1 divides to join us the given points that means the point of division given to be minus 9, 1. We can equate the abscissa of the ordinate as we can equate the x coordinate of this point with the value of x and the y coordinate of this point with the value of y. We equate the x coordinate with the value of x we get lambda minus 4 this whole point lambda plus 1 is equal to minus 9. Now further we get lambda minus 4 is equal to minus 9 into lambda plus 1 we hold this gives us lambda minus 4 is equal to 9 lambda minus 9. Transposing minus 9 lambda to the left hand side we get lambda plus 9 lambda is equal to plus 4 that is we have transposed. This gives us up is equal to minus and further lambda is equal to minus 5 upon lambda equal to minus 1 upon 2 value of lambda to be negative. The division is the required ratio to be lambda is to 1 and we get the value of lambda is minus 1 upon 2. So the required ratio is 1 is to 2 that the point minus 9, 1 the points minus 4 this we got the value of lambda to be negative that's why the division is external. This completes the session hope you have understood the solution of this question.