Question

$ABC$ is a triangle $G$ is the centroid $ D$ is the mid- point of $BC$. If $A - (2, 3) $ and $G = (7, 5)$, then the point $D$ is

• A. $ \left(\frac {19}{2},6\right)$
• B. $ \left(\frac {9}{2},4\right)$
• C. $\left(8, \frac{13}{2}\right)$
• D. $ \left(\frac {11}{2},\frac{11}{2}\right)$

Answer 1

Answer: (A)

Since, D is the mid point of BC. So, coordinate of
$BC$ are $\left(\frac{x_{2} + x_{3} }{2} , \frac{y_{2} +y_{3}}{2}\right)$
Given, $G (7, 5)$ is the centroid of $\Delta \,ABC $
$ \therefore 7 = \frac{2+ x_{2} + x_{3}}{3}$
and $5 = \frac{3+y_{2} + y_{3}}{3} $
$\Rightarrow x_{2} + x_{3} = 21-2$
and $ y_{2} + y_{3} = 15 -3 $
$ \Rightarrow x_{2} + x_{3} = 19$
and $ y_{2 } +y_{3} = 12 $

$ \Rightarrow \frac{x_{2} +x_{3}}{2} = \frac{19}{2}$
and $ \frac{y_{2} + y_{3} }{2} = 6 $
$\therefore $ Coordinate of D are $\left( \frac{19}{2} , 6 \right)$