Question

If $G$ is the centroid of the $△ABC$ and $G^{\prime }$ is the centroid of the $△A^{\prime }{B}^{\prime }{C}^{\prime }$, then $A{A}^{\prime }+B{B}^{\prime }+C{C}^{\prime }$ is

• A. $G{G}^{\prime }$
• B. $2G{G}^{\prime }$
• C. $3G{G}^{\prime }$
• D. None of these

Answer 1

Answer: (C)

$3G{G}^{\prime }$

We know that by defination and formula of centriod

$OA+OB+OC=3OG$

and $O{A}^{\prime }+O{B}^{\prime }+O{C}^{\prime }=3O{G}^{\prime }$

So,

$\therefore A{A}^{\prime }+B{B}^{\prime }+C{C}^{\prime }$

$O{A}^{\prime }-OA+O{B}^{\prime }-OB+O{C}^{\prime }-OC$

$=3O{G}^{\prime }-3OG=3G{G}^{\prime }$