two coordinates and equation of centroid is given then find third vertex

Suppose a triangle ∆ABC is given where A(a,b) and B(c,d) are the two points of the triangle. The centroid of the triangle is given as G(p,q), then the third vertex C(x,y) is required to be known.

 

Centroid of a traingle is given by, G=[ A+B+C]÷3

                     That is, 

                                (p,q)= ([a+c+x]÷3, [b+d+y]÷3)

 

Now the coordinates of point C are given by,

        (x,y)= (3p-a-c,3q-b-d) 

 

Hence by substituting the given points in the formula gives you the answer

 

Harsha