Question

Find the third vertex a ∆ABC if two of its vertices are B(−3, 1) and C(0, −2) and its centroid is at the origin.

Answer 1

Two vertices of ABC are B(- 3, 1) and C(0, -2). Let the third vertex be A(a, b).
Then, the coordinates of its centroid are
$G\left(\frac{-3+0+a}{3},\frac{1-2+b}{3}\right)$
$=G\left(\frac{-3+a}{3},\frac{-1+b}{3}\right)$
But is is given that the centroid is G(0,0).
Therefore, $\frac{-3+a}{3}=0$ and $\frac{-1+b}{3}=0$
⇒ - 3+ a = 0 and - 1+ b = 0
⇒ a = 3 and b = 1
Hence, the third vertex of ∆ABC is A(3 ,1).