Question

Given $A(1,3)$ and $B(7,-3)$ points on xy-plane. $A$ point $P$ is taken on $AB$ 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

• A. $\left(\frac{71}{5},\frac{51}{5}\right)$
• B. $\left(\frac{71}{5},\frac{-51}{5}\right)$
• C. $\left(\frac{51}{5},\frac{71}{5}\right)$
• D. $\left(\frac{-51}{5},\frac{71}{5}\right)$

Answer 1

Answer: (B)

$x=\frac{14+3}{5}=\frac{17}{5};$
$y=\frac{-6+9}{5}=\frac{3}{5}$

$x_1=\frac{3\times 7-2\times \frac{17}{5}}{3-2}=\frac{105-34}{5};$
$x_1=\frac{71}{5}$
$y_1=\frac{3\times (-3)-2\left(\frac{3}{5}\right)}{3-2};$
$y_1=-9-\frac{6}{5}$
$\Rightarrow y_1=\frac{-51}{5}$
Hence, $Q\left(\frac{71}{5},\frac{-51}{5}\right)$