Question

If two vertices of a triangle are $(-1,4)$ and $(5,2)$ and its centroid is $(0,-3)$, then the third vertex is

• A. $(4,15)0$
• B. $(-4,-15)$
• C. $(2,16)$
• D. $(-2,-16)$

Answer 1

Answer: (B)

Let the third vertex be $(x,y)$. Then, the coordinates of the centroid of triangle are
$\left(\frac{-1+5+x}{3},\frac{4+2+y}{3}\right)\text{ i.e., }\left(\frac{4+x}{3},\frac{6+y}{3}\right)\text{. }$
Now, $\left(\frac{4+x}{3},\frac{6+y}{3}\right)=(0,-3)$
$\Rightarrow \frac{4+x}{3}=0$ and $\frac{6+y}{3}=-3$
$\Rightarrow 4+x=0$ and $y+6=-9$
or $x=-4$ and $y=-15$
Hence, the third vertex is $(-4,-15)$.