 Hi and welcome to your session. Let us discuss the following question. The question says in what ratio the line joining minus 1, 1 and 5, 7 is divided by the line x plus y is equal to 4. Suppose AB is the line which is formed by joining points minus 1, 1 and 5, 7. This is the line whose equation is x plus y is equal to 4. This line is intersecting this line at point p and dividing this line in some ratio and we have to find the ratio in which this line divides AB. Let's now begin with the solution. Let the required ratio be k is to 1. Let p has coordinates x1, y1. We have learned in the section formula that coordinates of a point that is p, which divides the line segment in the ratio m is to n are x is equal to m x2 plus n x1 upon m plus n and y is equal to m y2 plus n y1 upon m plus n. Now here x1, y1 is minus 1, 1. x2, y2 is 5, 7. And coordinates of p are x1, y1. So by using section formula x1 is equal to k into 5 plus 1 into minus 1 upon k plus 1 and y1 is equal to k into 7 plus 1 into 1 upon k plus 1. Now since x1, y1 lies on line x plus y is equal to 4. Therefore it must satisfy this equation thus now we have 5k minus 1 upon k plus 1 plus 7k plus 1 upon k plus 1 is equal to 4. Now this implies 5k minus 1 plus 7k plus 1 is equal to 4 into k plus 1. This implies 12k is equal to 4k plus 4 and this implies k is equal to 1 by 2. Hence the required ratio is 1 is to 2. This is our required answer. So this completes the session. Bye and take care.