 Hi and welcome to our session. Let us discuss the following question. The question says, in the triangle ABC with vertices A having coordinates 2, 3, B 4 minus 1 and C 1, 2, find the equation and length of altitude from the vertex A. Now this is the triangle ABC, A is having coordinates 2, 3, B is having coordinates 4 minus 1 and C is having coordinates 1, 2. We have to find the equation and length of altitude from the vertex A. That means we have to find the equation and length of A n. Let us start with the solution. First find slope of line BC. Now slope of line BC is equal to 2 minus minus 1 upon 1 minus 4 and this is equal to 3 by minus 3. This is equal to minus 5. Now since A n is perpendicular to BC, therefore slope of A n into slope of BC is equal to minus 1. Now slope of BC is minus 1. So this implies slope of A n is equal to 1 because product of slopes of two perpendicular lines is minus 1. Now we will find equation of A n. Now A n is passing through the point 2, 3 and is having slope m. So we can now easily find the equation of A n. So equation of A n which passes through having coordinates 2, 3 and slope 1 is y minus 3 is equal to 1 into x minus 2. Now this implies y minus 3 is equal to x minus 2. And this implies x minus 5 plus 1 is equal to 0. So equation of A n is x minus 5 plus 1 is equal to 0. Right. Now we have to find length of A n. Now A n is the perpendicular distance of point A from the line BC. So let's now find the equation of line BC. Now BC is passing through 0.4 minus 1 and is having slope minus 1. So equation of BC is x plus 1 is equal to minus 1 into x minus 4. This implies x plus 5 minus 3 is equal to 0. You know that length of altitude A n is equal to perpendicular distance point A having coordinates 2, 3 to BC. Now perpendicular distance from point A having coordinates 2, 3 to BC is 1 into 2 plus 1 into 3 minus 3 upon square root of 1 square plus 1 square. Now this is equal to 2 plus 3 minus 3 upon square root of 2 and this is equal to 2 by root 2 and this is equal to root 2. So length of altitude A n is root 2. Hence the required equation of altitude is y minus x is equal to 1 and its length is root 2. This is our required answer. So this completes the session bye and take care.