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) 

\[- 4 = \left( \frac{- 14 + 3 + x}{3} \right)\]

\[ \Rightarrow - 12 = x - 11\]

\[ \Rightarrow x = - 1\]

\[\text { Also }, \]

\[ - 7 = \left( \frac{- 19 + 5 + y}{3} \right)\]

\[ \Rightarrow - 21 = - 14 + y\]

\[ \Rightarrow y = - 7\]

Thus, point C will be 

\[\left( - 1, - 7 \right)\].