 Hello and welcome to the session. Let's work out the following problem. It says two vertices of a triangle are 3, 5 and minus 2, 4. If the centroid is 5, 6 then find the third vertex. So let's now move on to the solution. You have to find the third vertex of the triangle, so let the third vertex of triangle be xy. Now as 5, 6 is the centroid therefore 5 is equal to sum of the x-coordinate of the three vertices, that is 3 plus minus 2 plus x upon 3 and 6 is equal to the sum of the y-coordinate of the three vertices upon 3, that is 5 plus 4 plus y, since the third vertex has y-coordinate as y itself upon 3. As we know that if we have a triangle say a, b, c with vertices x1, y1, x2, y2, x3, y3 and xy is the centroid then x is given by x1 plus x2 plus x3 upon 3 and y is equal to y1 plus y2 plus y3 upon 3. You must remember this formula. So we have 5 is equal to 3 plus minus 2 plus x upon 3, 6 is equal to 5 plus 4 plus y upon 3. So this implies 15 is equal to 1 plus x and this implies 18 is equal to 9 plus y. So this implies x is equal to 15 minus 1 and this implies y is equal to 18 minus 9. So this implies x is equal to 14 and from this we have y is equal to 9. Hence the third vertex of triangle is 14, 9. So this completes the question and the session. Why for now take care. Have a good day.