 Hello and welcome to the session. In this session we will discuss a question which says that if A1, 2, D4, 3 and C6, 6 are three purposes of a parallelogram A, B, C, D, find the coordinates of the fourth vertex D and the option R, option A, 3, 5, option B, 5, 3, option C, 6, 10, option D, 3, 3. Now before starting the solution of this question, we should know some results. And that are the midpoint formula. If A, B is the line segment with C as the midpoint of A, B and the coordinates of A are x1, y1, coordinates of B are x2, y2, then by midpoint formula, coordinates of C are x1, x2, y2 and y1, this y2, y2. Here C is the midpoint and diagonals of a parallelogram bisect each other. Now these results will work out as a key idea for figuring out this question. And now we will start with the solution. Here a parallelogram A, B, C, D is given to us in which the coordinates of A, B and C are given and we have to find the coordinates of T. Now let the coordinates of D as xy. And let us take the quantum interception of A, C and B, T, S. Now using this result, we can write as the diagonals of parallelogram bisect each other. Here in the parallelogram A, B, C, D, the diagonals are bisecting each other at point O. That is, O is the midpoint of A, C and P, T. So we can write the coordinates of midpoint of A, C is equal to coordinates of midpoint. Now by using the midpoint formula, we can find the coordinates of the midpoint. Which implies for finding out the coordinates of midpoint of A, C, we will continue to point A and C. And by using this, we have the coordinates of midpoint as 1 plus 6 by 2. That means x1 plus x2 by 2, 2 plus 6 by 2. That is, y1 plus y2 by 2 is equal to... Now for finding out the coordinates of midpoint of VD, we will consider the point V and D. And by using this, the coordinates of midpoint are x plus 4 by 2 and y plus 3 by 2. This implies 7 by 2, 8 by 2 is equal to x plus 4 by 2 and y plus 3 by 2. Which further implies 7 by 2 and 4 is equal to x plus 4 by 2 and y plus 3 by 2. Now since these two are equal, so equation where x coordinates V here plus 4 by 2 is equal to 7 by 2. Which further implies here 2 and 2 will be cancelled. So x is equal to 7 minus 4, which is equal to 3. Also, equating the y coordinates, we get 1 plus 3 by 2 is equal to 4. Which further implies y plus 3 is equal to 8, which gives y is equal to 5. Therefore, of D, so putting the values of x and y here, so the coordinates of D are 3, 5. So the answer of this question is option A. The answer is option A, which is equal to 3, 5. So this is the solution of the given question and that's all for this session. Hope you all have enjoyed the session.