 Hello and welcome to the session. In this session we will discuss a question which says that if r whose coordinates are x, y is a point on the line p with coordinates a, b and q with coordinates b, a, then prove that x plus y is equal to a plus b. Now before starting the solution of this question, we should know our result. And that is the three points p, x1, y1, q, x2, y2 and r, xc, y3 are collier area formed by these three points. Now we know that the area of the triangle pkr is given by 1, 2, x1 into y2 minus y3 the whole plus x2 into y3 minus y1 the whole plus x3 into y1 minus y2 the whole. Now if pkr will be collinear then this area will be equal to 0 which implies 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. So the points will be collinear that means they will lie on the same line if these three points will be equal to 0 that means when this condition holds. Now this result will work out as a t-idea for solving out this question and now we will start with the solution. Now it is given that r is the point on the line segment drawing the points p and q. So we have taken the point r on the line segment drawing the points p and q that x plus y is equal to a plus p. Now mq are the points which are lying the same line that means p, r and q are collier. Now we will use the condition of collinearity which is given in the t-idea. Now let us take the point p as x1 y1 x2 y2 and point q as x3 y3 and q are collier x1 into y2 minus y3 the whole plus x2 into y3 minus y1 the whole into y1 minus y2 the whole is equal to 0. Now putting the values of x1 y1, x2 y2 and x3 y3 here this implies a into y minus a the whole is b the whole plus b into b minus y the whole is equal to 0. minus a square plus a x minus b x minus b y is equal to 0. Further this can be written as plus a x minus b x minus b y plus b square these two terms taking a common it would be a into x plus y the whole and from these two terms taking minus b common it would be minus b into m's on the other side it would be a square minus b square. Now this implies x plus y the whole into a minus b the whole is equal to now this is the formula of a square minus b square which is equal to a plus b the whole into a minus b square. Further this implies x plus y is equal to a plus b the solution of a given question and that's all for this session hope you all have enjoyed this session.