Question

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

$Q(1,7),R(-3,1)$ and $m:n=1:2$

• A. $(\frac{-5}{3},3)$
• B. $(\frac{-5}{3},5)$
• C. $(\frac{-1}{3},3)$
• D. $(\frac{-1}{3},5)$

Answer 1

The correct option is D $(\frac{-1}{3},5)$

Let the co-ordinates of the point $P$ be $P(x,y)$ which divides the line segment $QR$ joining the points $Q(x_1,y_1)=(1,7)$

and $R(x_2,y_2)=(-3,1)$ in the ratio $m:n=1:2$.

Then by the section formula,

$x=\frac{n{x}_1+m{x}_2}{m+n}=\frac{2\times \left(1\right)+1\times (-3)}{1+2}=-\frac{1}{3}$ and

$y=\frac{n{y}_1+m{y}_2}{m+n}=\frac{2\times 7+1\times 1}{1+2}=5$

$\therefore P(x,y)=P(-\frac{1}{3},5)$