Question

Find the coordinates of the point $P$ which divides line segment $QR$ internally in the ratio $m:n$, where

$Q\equiv (6,-5),R\equiv (-10,2)$ and $m:n=3:4$

• A. $(\frac{22}{7},-1)$
• B. $(\frac{22}{7},2)$
• C. $(\frac{-6}{7},-2)$
• D. $(\frac{-6}{7},-1)$

Answer 1

Answer: (C)

$(\frac{-6}{7},-2)$

Let the co-ordinates of the point P be $P(x,y)$ which divides the line segment QR

joining the points $Q(x_1,y_1)=(6,-5)$ & $R(x_2,y_2)=(-10,2)$ in the ratio $m:n=3:4$

Then, by the section formula,

$x=\frac{n{x}_1+m{x}_2}{m+n}=\frac{4\times \left(6\right)+3\times (-10)}{3+4}=-\frac{6}{7}$ and

$y=\frac{n{y}_1+m{y}_2}{m+n}=\frac{4\times (-5)+3\times 2}{3+4}=-2$

$\therefore P(x,y)=P(-\frac{6}{7},-2)$