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

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

KEAMKEAM 2013Straight Lines

Solution:

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