Question

In $△$ABC , G(-4, -7) is the centroid. If the coordinates of A and B are (-14, -19) and (3, 5) respectively, then find the co-ordinates of C.

• A. (-1, 7)
• B. (-1, -7)
• C. (-2, -7)
• D. (1, 7)

Answer 1

The correct option is B (-1, -7)

Given:
Centroid, $G(-4,-7)$
Vertex, $A(-14,-19)\&B(3,5)$

Let the Co-ordinates of $C$ be $(x_3,y_3)$
$x_1=-14,x_2=3,y_1=-19\&y_2=5$

Centroid
$G(-4,-7)=(\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3})$

$\Rightarrow \frac{-14+3+x_3}{3}=-4$
$\Rightarrow x_3-11=-12\Rightarrow x_3=-1$

and $\frac{-19+5+y_3}{3}=-7$
$\Rightarrow y_3-14=-21\Rightarrow y_3=-7$

$\therefore$ Co-ordinates of $C$ are $(-1,-7)$