Two vertical of a ΔABC are given by A(6, 4) and B (– 2, 2) and its centroid is G(3, 4). Find the coordinates of its third vertex C.
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).