 Hi and welcome to our session. Let us discuss the following question. The question says if the origin is the centroid of the triangle PQR with vertices P having coordinates 2, A, 2, 6, Q having coordinates minus 4, 3, V, minus 10 and R having coordinates A, 14, 2, C then find the values of A, B and C. Before solving this question we should know that if A having coordinates x1, y1, z1, V having coordinates x2, y2, z2 and C having coordinates x3, y3, z3 are the vertices of a triangle A, B, C then coordinates of the centroid of the triangle A, B, C will be x1 plus x2 plus x3 by 3, y1 plus y2 plus y3 by 3, z1 plus z2 plus z3 by 3. The knowledge of this is the key idea in this question. Now we begin with the solution. We have given that PQ and R are three vertices of the triangle PQR and we are also given that its centroid is at the origin. Using this information we have to find the values of A, B and C. We will first find coordinates of the centroid of the triangle PQR. Key idea we know that if A having coordinates x1, y1, z1, B having coordinates x2, y2, z2 and C having coordinates x3, y3, z3 then coordinates of the centroid of triangle A, B, C is given by x1 plus x2 plus x3 by 3, y1 plus y2 plus y3 by 3, z1 plus z2 plus z3 by 3. So using this coordinates of the centroid of the triangle PQR will be 2A minus 4 plus 8 by 3, 2 plus 3B plus 14 by 3, 6 minus 10 plus 2C by 3. This is equal to 2A plus 4 by 3, 3B plus 16 by 3 minus 4 plus 2C by 3. But we are given that the coordinates of the triangle PQR 0, 0, 0 since the centroid is at the origin. Hence equating corresponding y, z coordinates we get plus 4 by 3 is equal to 0, 16 plus 3B by 3 is equal to 0, minus 4 plus 2C by 3 is equal to 0. Now 2A plus 4 by 3 equals to 0 implies A is equal to minus 2, 16 plus 3B by 3 equals to 0 implies B is equal to minus 16 by 3, minus 4 plus 2C by 3 equals to 0 implies C is equal to 2. Hence the required value of A is minus 2, value of B is minus 16 by 3 and value of C is 2. This is our required answer. So this completes the session. Bye and take care.