Question

Let $G$ and $G^1$ be the centroids of the triangles $ABC$ and $A^1{B}^1{C}^1$ respectively, then $A{A}^1+B{B}^1+C{C}^1$ is equal to

• A. $2G{G}^1$
• B. $3G^{1}G$
• C. $3G{G}^1$
• D. $\frac{3}{2}G{G}^1$

Answer 1

The correct option is C $3G{G}^1$

$G=\frac{A+B+C}{3}\Rightarrow A+B+C=3G$ ......(1)

and $G^1=\frac{A^1+B^1+C^1}{3}\Rightarrow A^1+B^1+C^1=3G^1$ ......(2)

$\therefore A{A}^1+B{B}^1+C{C}^1=(A-A^1)+(B-B^1)+(C-C^1)$

$=(A+B+C)-(A^1+B^1+C^1)$

$=3G-3G^1=3(G-G^1)=3G{G}^1$, Using (1) and (2)