Question

A(h, -6), B(2, 3) and C(-6, k) are the co-ordinates of vertices of a triangle whose centroid is G (1, 5). Find h and k.

Answer 1

$A(x_1,y_1)=A(h,-6)$
$B(x_2,y_2)=B(2,3)$
$C(x_3,y_3)=C(-6,k)$
$\therefore$ centroid G (x, y) = G (1, 5)
G is the centroid.
By centroid formula,
$x=\frac{x_1+x_2+x_3}{3}$
$\therefore 1=\frac{h+2+(-6)}{3}$
$\therefore 3=h+2-6$
$\therefore 3=h+4$
$\therefore h=3+4$
$\therefore h=7$
$y=\frac{y_1+y_2+y_3}{3}$
$\therefore 5=\frac{-6+3+k}{3}$
$\therefore 15=-3+k$
$\therefore k=15+3$
$\therefore k=18$
$\therefore h=7andk=18$