Question

Find the third vertex of a triangle whose centroid is $(1,4)$ and two vertices are $(-1,4)$ and $(3,-1)$.

• A. $(1,3)$
• B. $(2,3)$
• C. $(7,3)$
• D. $(1,9)$

Answer 1

The correct option is D $(1,9)$

Let the third vertex be $(x,y)$, we have
$\because x_c=\frac{x_1+x_2+x_3}{3}\Rightarrow \frac{x-1+3}{3}=1\Rightarrow x=1$
$y_c=\frac{y_1+y_2+y_3}{3}\frac{y+4-1}{3}=4\Rightarrow y=9$
The third vertex is $(1,9)$.