 Hello and welcome to the session. My name is Asha and I am going to help you with the last question of this exercise which says, find the coordinates of the points which trisect the line segment joining the points P and Q or trisect means to divide the line segment into three equal parts. We have to find the points A and B such that A divides the line segment first in the ratio 1 is to 2 and then we shall find the coordinates of the point B which divides the line segment P, Q and the ratio 2 is to 1. So we shall find the coordinates of point A and B with the help of section formula. This is our key idea. Let us now start with the solution. Now, let point A divides the line segment P, Q and the ratio 1 is to 2. Then, let the coordinates of A, B, X, Y and Z. Then by the section formula, the coordinates X, Y and Z are given by 1 into 10 plus 2 into 4 upon 1 plus 2 then to find the Y coordinate 1 into minus 16 plus 2 into 2 upon 1 plus 2 and the Z coordinate is given by 1 into 6 plus 2 into minus 6 upon 1 plus 2 or XY and Z are further equal to 6 minus 4 and minus 2. So the coordinates of point A are 6 minus 4 and minus 2. Now let us find the coordinates of point B and the coordinates P, X dash, Y dash and Z dash. Again, by the section formula, X dash, Y dash and Z dash are given by 2 into 10 plus 1 into 4 upon 2 plus 1 then the Y dash coordinate is 2 into minus 16 plus 1 into 2 upon 2 plus 1 and the Z coordinate is 2 into 6 plus 1 into minus 6 upon 2 plus 1. Please refer to the earlier questions of this exercise to understand the section formula properly or this further implies that X dash, Y dash and Z dash is equal to 8 minus 10 and 2. So these are the coordinates of point B which divides the line segment PQ in the ratio 2 is 2 1 and this is when B divides PQ in the ratio 2 is 2 1. Hence the coordinates of the points which trisect the line segment PQ are 6 minus 4 minus 2 and 8 minus 10 2. Thus our answer is 6 minus 4 minus 2 and 8 minus 10 and 2. So this completes the session. Hope you have understood it. Take care and have a good day.