Question

$A(-5,2),B(x,-3)$ and $C(-2,y)$ are the vertices of $\Delta ABC$. G is a centroid of $\Delta ABC$. The coordinates of $G$ are $G(-2,1)$. Then find the value of $x$ and $y$.

• A. $x=1$ and $y=4$
• B. $x=-2$ and $y=-4$
• C. $x=1$ and $y=-3$
• D. $x=-1$ and $y=-4$

Answer 1

The correct option is A $x=1$ and $y=4$

If $A(x_1,y_1),B(x_2,y_2),C(x_3,y_3)$ are vertices of $\Delta ABC$.

$G(x,y)$ is the centroid of $\Delta ABC$.

Then,
$G=(\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3})$

Given that $A(-5,2),B(x,-3)$ and $C(-2,y)$ are vertices of $\Delta ABC$.
$G(-2,1)$ is the centroid of $\Delta ABC$.

Then.

$(-2,1)=(\frac{-5+x-2}{3},\frac{2-3+y}{3})$
$\therefore -2=\frac{x-7}{3}$ and $1=\frac{y-1}{3}$

$\therefore -6=x-7,3=y-1$
$\therefore x=1$ and $y=4$