Question

The point which divides the line segment joining the points $(6,3)$ and $(-4,5)$ in the ratio $3:2$ externally is

• A. $(5,-8)$
• B. $(6,9)$
• C. $(8,25)$
• D. $(-24,9)$

Answer 1

The correct option is D $(-24,9)$

Let $A=(6,3),B=(-4,5)$ and the required point which divides the line segment in ratio of $3:2$ externally be $P=(x,y)$

For external division, we have
$x=\frac{3(-4)-2\left(6\right)}{3-2}y=\frac{3\left(5\right)-2\left(3\right)}{3-2}$
$\Rightarrow x=-24,y=9$

Hence, the required coordinates are $(-24,9)$.