Question

Let $O$ be the origin and $A$ be the point $(64,0)$. If $P$ and $Q$ divide $OA$ in the ratio $1:2:3$, then the point $P$ is

• A. $(\frac{32}{3},0)$
• B. $(32,0)$
• C. $(\frac{64}{3},0)$
• D. $(16,0)$
• E. $(\frac{16}{3},0)$

Answer 1

The correct option is A $(\frac{32}{3},0)$

Now, by internal section formula,
$P\equiv (\frac{1\times 64+5\times 10}{1+5}\cdot \frac{1\times 0+5\times 0}{1+5})$
$\equiv (\frac{64}{6},0)=(\frac{32}{3},0)$.