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  4. Given A (1,3) and B (7,-3) points on xy-plane. A point P is taken on A B dividing it internally in the ratio 2: 3. A point Q divides PB externally in the ratio 3: 2, then co-ordinates of point Q is

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Q. Given $A (1,3)$ and $B (7,-3)$ points on xy-plane. $A$ point $P$ is taken on $A B$ dividing it internally in the ratio $2: 3.$ A point $Q$ divides $PB$ externally in the ratio $3: 2$, then co-ordinates of point $Q$ is

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Solution:

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$x =\frac{14+3}{5}=\frac{17}{5} ; $
$y =\frac{-6+9}{5}=\frac{3}{5}$
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$ x _{1}=\frac{3 \times 7-2 \times \frac{17}{5}}{3-2}=\frac{105-34}{5} ;$
$ x _{1}=\frac{71}{5} $
$y _{1}=\frac{3 \times(-3)-2\left(\frac{3}{5}\right)}{3-2} ; $
$y _{1}=-9-\frac{6}{5} $
$\Rightarrow y _{1}=\frac{-51}{5}$
Hence, $Q \left(\frac{71}{5}, \frac{-51}{5}\right)$