Answer :

Let the third vertex C ≡ (x3,y3)


In a Δ ABC,


Vertex A ≡ (x1,y1) ≡ (6,4)


Vertex B ≡ (x2,y2) ≡ (– 2,2)


Centroid(G) ≡ (x,y) ≡ (3,4)


Centroid of a Δ ABC is given by –


x = (x1 + x2 + x3)/3


3 = (6 – 2 + x3)/3


9 = 4 + x3


x3 = 5


And,


y = (y1 + y2 + y3)/3


4 = (4 + 2 + y3)/3


12 = 6 + y3


y3 = 6


Thus, the coordinates of third vertex C is (5,6).


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