Question

If $(\frac{5}{3},3)$ is the centroid of a triangle and its two vertices are $(0,1)$ and $(2,3)$, then the coordinates of the third vertex are

• A. $(1,2)$
• B. $(2,3)$
• C. $(3,4)$
• D. $(3,5)$

Answer 1

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

Let the third vertex of triangle be $(x,y)$, then
$\frac{x+0+2}{3}=\frac{5}{3}\text{and}\frac{y+1+3}{3}=3\Rightarrow x=3,y=5$

Hence, the third vertex is $(3,5).$