Question

Find the co-ordinates of the point $P$ which divides segment $JL$ externally in the ratio $m:n$ in the following example:

$J(5,-3),L(0,9),m:n=4:3$

• A. $(-15,45)$
• B. $(15,-45)$
• C. $(15,45)$
• D. $(-15,-45)$

Answer 1

The correct option is A $(-15,45)$

Let the co-ordinates of the point $P$ be $P(x,y)$ which divides the line segment $JL$ joining the points $J(x_1,y_1)=(5,-3)\&L(x_2,y_2)=(0,9)$ in the ratio $m:n=4:3$

Then, by the section formula, $x=\frac{n{x}_1-m{x}_2}{n-m}=\frac{3\times 5-4\times 0}{3-4}=-15$ and

$y=\frac{n{y}_1-m{y}_2}{n-m}=\frac{3\times (-3)-4\times 9}{3-4}=45$

$\therefore P(x,y)=P(-15,45)$