Question

In △ABC, G (-4, -7) is the centroid. If A (-14, -19) and B(3, 5) then find the co-ordinates of C.
$\left[3\right]$

Answer 1

Solution:
Let the coordinates of point C be (x, y).
Centroid = G(-4,-7)

We know if $(x_1,y_1),(x_2,y_2)$ and $(x_3,y_3)$ are the vertices of a triangle then the co-ordinates of the centroid are $(\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3})$.
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$\therefore$ -4 =$\frac{(-14+3+x_3)}{3}$
$\Rightarrow x_3-11=-12$
$\Rightarrow x_3=-1$
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Similarly,
-7 =$\frac{(-19+5+y_3)}{3}$
$\Rightarrow y_3-14=-21$
$\Rightarrow y_3=-7$

So, the coordinates of point C are (-1, -7).
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