Question

In $\Delta ABC$, if $A(1,-6),B(-5,2)$ and the centroid is $G(-2,1)$, then Co-ordinates of vertex $C$ are

• A. $(-2,1)$
• B. $(-2,6)$
• C. $(3,2)$
• D. $(-2,7)$

Answer 1

Answer: (D)

$(-2,7)$

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

$G(-2,1)=(\frac{1-5+x_3}{3},\frac{-6+2+y_3}{3})$

$G(-2,1)=(\frac{-4+x_3}{3},\frac{-4+y_3}{3})$

$\Rightarrow \frac{-4+x_3}{3}=-2,\frac{-4+y_3}{3}=1$

$\Rightarrow -4+x_3=-6,-4+y_3=3$

$\Rightarrow x_3=-6+4=-2,y_3=3+4=7$

Hence the third vertex is $(-2,7)$