Find the third vertex of a Δ ABC if two of its vertices are

B (– 3, 1) and C (0, – 2) and its centroid is at the origin.

Let the third vertex A ≡ (x1,y1)


In a Δ ABC,


Vertex B ≡ (x2,y2) ≡ (– 3,1)


Vertex C ≡ (x3,y3) ≡ (0, – 2)


Centroid(G) ≡ (x,y) ≡ (0,0)


Centroid of a Δ ABC is given by –


x = (x1 + x2 + x3)/3


⇒ 0 = (x1 – 3 + 0)/3


⇒ 0 = x1 – 3


∴ x1 = 3


And,


y = (y1 + y2 + y3)/3


⇒ 0 = (y1 + 1 – 2)/3


⇒ 0 = y1 – 1


∴ y1 = 1


Thus, the coordinates of third vertex A is (3,1).


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