Question

If the centroid of the triangle formed by $(7,x),(y,-6)$ and $(9,10)$ is at $(6,3)$, then $(x,y)$ is :

• A. (5, 2)
• B. (3, 1)
• C. (4, 0)
• D. (1, 3)

Answer 1

The correct option is A (5, 2)

Given, centroid of the triangle = $(6,3)$

$\because$ 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,
$(x_1,y_1)=(7,x)(x_2,y_2)=(y,-6)(x_3,y_3)=(9,10)$

$\therefore (6,3)=(\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3})\Rightarrow \frac{x+(-6)+10}{3}=3\Rightarrow x+4=9\Rightarrow x=5$

and $\frac{7+y+9}{3}=6$
$\Rightarrow y+16=18\Rightarrow y=2\therefore (x,y)=(5,2)$