Question

Two vertices of ∆ABC are A(6, 4) and B(−2, 2) and its centroid is G(3, 4). Find the coordinates of its third vertex C.

Answer 1

Two vertices of ΔABC are A(6, 4) and B(− 2, 2). Let the third vertex be C(a, b).
Then, the coordinates of its centroid are
$G\left(\frac{6-2+a}{3},\frac{4+2+b}{3}\right)$
$\Rightarrow G\left(\frac{4+a}{3},\frac{6+b}{3}\right)$
But it is given that the centroid is G(3,4).
∴ $\frac{4+a}{3}=3$ and $\frac{6+b}{3}=4$
⇒ 4 + a = 9 and 6 + b = 12
⇒ a = 5 and b = 6
Hence, the third vertex of ΔABC is C(5, 6).