Question

Two vertices of a triangle are $A(1,1),B(2,-3)$. If its centroid is $(2,1)$, find the third vertex.

• A. $(3,5)$
• B. $(3,-5)$
• C. $(-3,5)$
• D. $(4,5)$

Answer 1

The correct option is A $(3,5)$

Let the co-ordinates of the third vertex be $(x,y)$.

Then, the coordinates of the centroid are $(\frac{1+2+x}{3},\frac{1-3+y}{3})=(\frac{3+x}{3},\frac{-2+y}{3})$
Given, $(\frac{3+x}{3},\frac{-2+y}{3})=(2,1)$
$\Rightarrow \frac{3+x}{3}=2$ and $\frac{-2+y}{3}=1$

$\Rightarrow 3+x=6$ and $-2+y=3$
$\Rightarrow x=3$ and $y=5$.
$\therefore$ Co-ordinates of the third vertex are $(3,5)$.