Question

In ∆ABC, G (–4, –7) is the centroid. If A (–14, –19) and B(3, 5) then find the co–ordinates of C.

Answer 1

Let the coordinates of point C be (x, y).
Centroid = G (–4, –7)
$$\begin{gathered} -4=\left(\frac{-14+3+x}{3}\right) \\ \Rightarrow -12=x-11 \\ \Rightarrow x=-1 \\ Also, \\ -7=\left(\frac{-19+5+y}{3}\right) \\ \Rightarrow -21=-14+y \\ \Rightarrow y=-7 \end{gathered}$$
Thus, point C will be $\left(-1,-7\right)$.