Question

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

• A. -11

Answer 1

The correct option is A -11
Given, centroid of the triangle = $(1,5)$

$\because$ The centroid of triangle formed by $(x_1,y_1),(x_2,y_2),(x_3,y_3)$ is $\left(\frac{x_1+x_2+x_3}{3}\right),\left(\frac{y_1+y_2+y_3}{3}\right)$

Here,
$x_1=h,x_2=2,\&x_3=-6y_1=-6,y_2=3\&y_3=k$

$\therefore (1,5)$ = $(\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3})$

$\Rightarrow 1=\frac{h+2+(-6)}{3}$

$\Rightarrow h-4=3\Rightarrow h=7$

and, $\frac{-6+3+k}{3}=5$

$\Rightarrow k-3=15\Rightarrow k=18$

$\therefore$ The value of h - k =7 - 18 = -11