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).