 Hello friends welcome to the session I am Alka. Let's discuss the given question if 1, 2, 4, 5, x, 6 and 3, 5 are the vertices of a parallelogram taken in order 5, x and y. Now before starting with the solution I would like to tell you the basic idea behind the solution. Let there are 2 points a and v. The coordinates of a are x1, y1 and that of v are x2, y2. So if p with the midpoint of the line joining a and v to the coordinates of the midpoint of line joining the 2 points is given by x1 plus x2 upon 2 and y1 plus y2 upon 2. According to the question here is the figure of a parallelogram a, b, c, d. The coordinates of a as 1, 2, b as 4 and y c as x and 6, d as 3 and 5. Now this is the figure according to the question with a, b, c, d as a parallelogram and the coordinates of a are 1, 2, v as 4, y, c, x, 6, d, 3, 5. Now we all know that the diagonals of a parallelogram bisect each other. So let's discuss the question further. Let a, b, c, d, v are parallelogram whose vertices with coordinates 1, 2, v with coordinates 4 and y, c with coordinates x and 6 and v with coordinates 3 and 5. Now since we know that the diagonals of parallelogram bisect each other therefore we can say that coordinates the midpoint of a, c equal to coordinates of the midpoint of b, d. So this can be written as 1 plus x that is 1 plus x upon 2 and 2 plus 6 upon 2. These are the coordinates of the midpoint of a, c and similarly we will write the coordinates of the midpoint of b, d that is x1 plus x2 upon 2 that is 4 plus 3 upon 2 and 5 plus y upon 2. This implies 1 plus x upon 2 and 8 upon 2 is 4 equal to 7 upon 2 and 5 plus y upon 2. Now we will compare the corresponding paths on comparing corresponding we get 1 plus x upon 2 equal to 7 upon 2. Here we see that 2, 2 cancel out and this implies 1 plus x equal to 7. This implies x equal to 7 minus 1. Therefore x equal to 6 and now on comparing the coordinates of y that is 4 equal to 5 plus y upon 2. So this implies 5 plus y equal to 8. This implies y equal to 3. Therefore we can say that x equal to 6 and y equal to 3 is the required answer. So hope you understood the solution and enjoyed the session. Goodbye and take care.