Question

Find the third vertex of a triangle, if two of its vertices are $(-3,1),(0,-2)$ and centroid is at the origin.

• A. $(3,4)$
• B. $(2,1)$
• C. $(3,2)$
• D. $(3,1)$

Answer 1

The correct option is D $(3,1)$

Let the third vertex be $(a,b)\equiv (x_1,y_1),(-3,1)\equiv (x_2,y_2),(0,-2)\equiv (x_3,y_3)$

Centroid of triangle is $(0,0)$

$G=[\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3}]$

$\Rightarrow (\frac{a-3+0}{3},\frac{b+1-2}{3})=(0,0)$

$\Rightarrow \frac{a-3}{3}=0$ and $\frac{b-1}{3}=0$

$\Rightarrow a=3,b=1$

So the third vertex is $(3,1)$