Question

Find the third vertex of triangle, if two of its vertices are $(5,7)$ and $(0,3)$ and centroid at origin.

• A. $10,5$
• B. $5,10$
• C. $-5,-10$
• D. $-10,-5$

Answer 1

The correct option is C $-5,-10$

Centroid $\Rightarrow \frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3}$

Centroid $\Rightarrow O(0,0)$ => $0=\frac{5+0+x_3}{3},0=\frac{7+3+y_3}{3}$

$x_3=-5,y_3=-10$

Third vertex $\equiv (-5,-10)$