 Hello and welcome to the session, the given question says A and B are two vertices of a triangle ABC whose centroid G has coordinates 5 by 3 and minus 1 by 3, find the coordinate of the third vertex C of the triangle. First let us learn the key idea behind this question with the help of which we shall find the third vertex C of a triangle. Suppose we have a triangle ABC then the centroid G whose coordinates x, y is equal to its x coordinate is given by x1 plus x2 plus x3 divided by 3 and y1 plus y2 plus y3 divided by 3 is the y coordinate of G. That is the x coordinate of the centroid is equal to the sum of x coordinates of the vertices of the triangle divided by 3 and similarly y coordinate of the centroid of a triangle is equal to the sum of y coordinates of the vertices divided by 3 and this problem we are given a triangle ABC whose the vertices of A and B are given and we have to find the third vertex C such that the centroid G is given by 5 by 3 comma minus 1 by 3. So let us move on to the solution. Here by the key idea we know that the coordinate of G that is 5 by 3 comma minus 1 by 3 is equal to the sum of x coordinates of the triangle ABC divided by 3 that is 3 plus minus 2 plus x divided by 3 and the y coordinate is given by 2 plus 1 plus y divided by 3 where C with coordinates x, y is the third vertex. Now let us solve this to find the value of x and y. Now on comparing the x coordinate we have 5 divided by 3 is equal to 1 plus x divided by 3 which implies that x is equal to 4 and on comparing the y coordinate we have minus 1 divided by 3 is equal to 3 plus y divided by 3 which gives y is equal to minus 4. Therefore we have x coordinate as 4 and y coordinate as minus 4. So this is the third vertex we have denoted by C so let us complete the session by intake Q.