Question

Find the vertex of triangle if two of its vertices are $(9,8)$ and $(-3,-5)$ and centroid at $(3,5)$.

• A. $12,3$
• B. $-12,-3$
• C. $3,12$
• D. $-3,-12$

Answer 1

The correct option is C $3,12$

Centroid $\Rightarrow \left(\begin{array}{c}\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3}\end{array}\right)$

$3=\frac{9-3+x_3}{3}$ and $5=\frac{8-5+y_3}{3}$

$9=9-3+x_3$ and $15=3+y_3$

$x_3=3$ and $y_3=12$

Third vertex $\equiv (3,12)$