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). Find the values of h and k.

• A. h = 18 and k = -7
• B. h = 5 and k = -7
• C. h = -7 and k = 18
• D. h = 7 and k = 18

Answer 1

The correct option is D h = 7 and k = 18

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

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