Question

Find the coordinates of the point which divides the line segment joining the points $(6,3)$ and $(-4,5)$ in the ratio $3:2$, externally.

• A. $(24,9)$
• B. $(-24,-9)$
• C. $(-24,9)$
• D. $(24,-9)$

Answer 1

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

Let P$(x,y)$ be the required point.
Using the section formula, if a point $(x,y)$ divides the line joining the points $(x_1,y_1)$ and $(x_2,y_2)$externally in the ratio $m:n$, then $(x,y)=(\frac{m{x}_2-n{x}_1}{m-n},\frac{m{y}_2-n{y}_1}{m-n})$
Substituting $(x_1,y_1)=(6,3)$ and $(x_2,y_2)=(-4,5)$ and $m=3,n=2$ in the section formula, we get

$P=(\frac{3(-4)-2\left(6\right)}{3-2},\frac{3\left(5\right)-2\left(3\right)}{3-2})=(-24,9)$