 Hello friends, welcome to the session on Malta. Let us discuss the given question. Find the coordinates of the points which divide the line segment joining A and B into 4 equal paths. Now let us begin with the solution. We are given a line segment AB and the coordinates of AR minus 2 and 2 and the coordinates of VR 2 and 8. Now we have to divide the given line segment into 4 equal paths. So P, Q and R. So let us assume that let P, Q and R divide line segment AB into 4 equal AB equal to P, Q equal to QR equal to RB. Now we can see from the figure that P divides AB in the ratio AB is to PB that is 1 is to 3P divides AB in the ratio AB is to PB that is 1 is to 3. Now we will apply the section formula to find the coordinates of the point P. So coordinates of point P1 into 2 plus 3 into minus 2 upon 1 plus 3 and my coordinate is 1 into 8 plus 3 into 2 upon 1 plus 3. So this is equal to minus 1 and 7 upon 2. Now we will find the coordinates of the point Q. Now here we see that Q divides the line segment AB in the ratio AQ is to, Q being that is 2 is to 2. So this implies that Q is the midpoint of the AB. Therefore we will find the coordinates of the point Q by midpoint formula. This we get by using section formula. Now from the figure we see that the point Q divides the line segment AB in the ratio AQ is to QB that is 2 is to 2 and this implies that Q is the midpoint of the line segment AB. Then we find the coordinates of the point Q by midpoint formula. Now Q divides AB in the ratio AQ is to QB that is 2 is to 2. So this implies that Q is the midpoint AB. Now we will find the coordinates Q. They are minus 2 plus 2 upon 2 and 2 plus 8 upon 2. So this is equal to 0 and 5. And this we get by using midpoint formula. We go for R. We see that R divides AB in the ratio AR is to RB that is 3 is to 1. Now we will find the coordinates. So we will find the coordinates of R by the section formula that will be 3 into 2 plus 1 into minus 2 upon 3 plus 1 and 3 into 8 plus 1 into 2 upon 3 plus 1. So this is equal to 1 and 13 by 2. Therefore coordinates of the points are minus 1, 7 by 2, 0, 5, 1 and 13 by 2. So hope you understood the solution and enjoyed the session. Goodbye and take care.