Question

If the coordinates of the centroid of a triangle are (1, 3) and two of its vertices are (-7, 6) and (8, 5) then the third vertex of the triangle is

• A. $(\frac{2}{3},\frac{14}{3})$
• B. $(-\frac{2}{3},-\frac{14}{3})$
• C. (2, -2)
• D. (-2, 2)

Answer 1

The correct option is C (2, -2)

Centroid of a triangle with vertices ${(x}_1,y_1);{(x}_2,y_2)$ and ${(x}_3,y_3)$ is calculated by the formula $(\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3})$

Let the third vertex of the triangle be $(x,y)$
So, centroid $=(\frac{-7+8+x}{3},\frac{6+5+y}{3})=(1,3)$
$=(\frac{1+x}{3},\frac{11+y}{3})=(1,3)$
$=>1+x=3;11+y=9$
$x=2;y=-2$
Hence the third vertex of the triangle is $(2,-2)$