Question

The centroid of a triangle is $(2,7)$ and two of its vertices are $(4,8)$ and $(-2,6).$ The third vertex is

• A. (0, 0)
• B. (4, 7)
• C. (7, 4)
• D. (7, 7)

Answer 1

The correct option is B

(4, 7)

Let $A(4,8)$ and $B(-2,6)$ be the given vertex. Let $C(h,k)$ be the third vertex.

The centroid of $\Delta ABC$ is $(\frac{4-2+h}{3},\frac{8+6+k}{3})$

It is given that the centroid of triangle ABC is $(2,7).$

$\therefore \frac{4-2+h}{3}=2,\frac{8+6+k}{3}=7$

$\Rightarrow h=4,k=7$

Thus, the third vertex is $(4,7)$