Question

If $(1,4)$ is the centroid of a triangle and two vertices are $(4,-3)$ and $(-9,7)$, then third vertices is:

• A. $(8,7)$
• B. $(7,8)$
• C. $(8,8)$
• D. $(6,8)$

Answer 1

The correct option is C $(8,8)$

Given centroid of triangle$=(1,4)$

Two vertices are $(4,-3)$ and $(-9,7)$

Let third vertex be $(a,b)$

$\therefore$Centroid=\left( \cfrac { a+4-9 }{ 3 } ,\cfrac { b+7-3 }{ 3 } \right) $

$\therefore \frac{a-5}{3}=1,\frac{b+4}{3}=4$

$a=8,b=8$

$\therefore$ Third vertex is $(8,8)$