 Hello and welcome to the session. In this session we will discuss a question which says that point P divides the line segment joining the points A21 and B5-8 such that AP over AB is equal to 1 over 3. If P lies on the line 2x-y plus k is equal to 0, find the value of k. Now before starting the solution of this question, we should know a result and that is the coordinates of a point P divided in the line segment joining the points Ax1y1 and Bx2y2 in the ratio m1 is to m2 are given by m1x2 plus m2x1 whole upon m1 plus m2 and m1y2 plus m2y1 whole upon m1 plus m2 and this formula is known as the section formula where this is the x coordinate of the point P and this is the y coordinate of the point P. Now this result will work out as a key idea for solving out this question and now we will start with the solution. Now it is given in the question that P divides the line segment joining the points A and B such that AP over AB is equal to 1 by 3. So given the coordinates of A21 and coordinates of B5-8 over AB is equal to 1 by 3. We have to find AP over PB. So it is given AP over AB is equal to 1 by 3. So let x which implies AP is equal to 3x. Now we have written as AP plus so AP is equal to AP so it will be 3x is equal to and AP is x where it will be x equal to 3x minus A AP over PB is 2x so this will be x which is equal to 1 by 2. Over PB is equal to 1 by 2 so we can write coordinates of P where we will use the section formula that is this formula which is given in the key idea. Now here let us take this ratio as m1 is to m2 coordinates of A as x1, y1 and coordinates of B as so by section formula of point P plus m2, x1 whole upon whole upon m1 plus mx1, y1, m1, m2 and x2, y2 here this will be equal to 1 into 5 plus 2 into 2 whole upon 1 plus 2 into minus 8 plus 2 into 1 whole upon 1 plus 2 which is further equal to plus 4 whole upon 3 over 3, 6 over 3. On further solving this will be equal to 3 and minus 2 therefore coordinates point P now it is given in the question that point P lies on y plus k is equal to 0 and then we have to find the value of k. So given lies on 2x minus y plus k is equal to 0 equal to 3 and y is equal to minus this applies 2 into 3 minus of minus 2 plus k this implies 6 plus k is equal to 0 which further implies 8 plus k is equal to 0 the required value of k of this question and that is all for this session hope you all have enjoyed the session.