 Hello and welcome to the session. In this session we discuss the following question which says if p with coordinates x and y is any point on the line joining the points a with coordinates a0 and b with coordinates 0b then show that x upon a plus y upon b is equal to 1. Before we move on to the solution let's recall the condition for the points say a point a with coordinates x1, y1 b with coordinates x2, y2 and point c with coordinates x3, y3 these three points would be collinear then the condition would be x1 into y2 minus y3 the whole plus x2 into y3 minus y1 the whole plus x3 into y1 minus y2 the whole is equal to 0. This is the key idea that we use for this question. Let's proceed with the solution now we are given a point p with coordinates xy this point p lies on the line joining the points a with coordinates a0 and b with coordinates 0b. So therefore we get that the points p with coordinates xy, a with coordinates a0 and b with coordinates 0b are collinear. Now as these three points are collinear so we will use this condition for the three points to be collinear and we substitute the values for x1, x2, x3, y1, y2, y3 and we get x into 0 minus b plus a into b minus y plus 0 into y minus 0 is equal to 0. Further we have minus bx plus ab minus ay is equal to 0 or you can say we have bx plus ay is equal to ab. Now dividing both sides by ab we get bx upon ab plus ay upon ab is equal to ab upon ab this b cancels with this b a cancels with a, ab cancels with ab so we left with x upon a plus y upon b is equal to 1 and this is what we were supposed to prove. So hence proved x upon a plus y upon b is equal to 1. This completes the session hope you have understood the solution of this question.