Question

A(h, –6), B(2, 3) and C(–6, k) are the co–ordinates of vertices of a triangle whose centroid is G (1, 5). Find h and k.

Answer 1

Centroid = G(1, 5)
The coordinates of the triangle are A(h, –6), B(2, 3) and C(–6, k).
$$\begin{gathered} 1=\left(\frac{h+2-6}{3}\right) \\ \Rightarrow 3=h-4 \\ \Rightarrow h=7 \\ Also, \\ 5=\left(\frac{-6+3+k}{3}\right) \\ \Rightarrow 15=k-3 \\ \Rightarrow k=18 \end{gathered}$$