Question

In what ratio does X-axis divide the line segment joining the points $(3,4)$ and $(2,6)$?

• A. $2:3$ internally
• B. $2:3$ externally
• C. $3:2$ internally
• D. $3:2$ externally

Answer 1

The correct option is B $2:3$ externally

Given the points $(3,4)$ and $(2,6)$

let the required ratio be $K:1$

$\Rightarrow$ By section formula

$x=\frac{m{x}_2+n{x}_1}{m+n},y=\frac{m{y}_2+n{y}_1}{m+n}$

As x-axis divides (x,y) will be of the form (x,0)

$x=\frac{2K+3}{K+1},y=\frac{6K+4}{K+1}\Rightarrow \frac{6K+4}{K+1}=0\Rightarrow 6K=-4\therefore K=\frac{-2}{3}\therefore 2:3$ externally

$\therefore$ putting the value of K in (x,Y)

$x=\frac{2K+3}{K+1}=\frac{2x-\frac{-2}{3}+3}{\frac{-2}{3}+1}=\frac{\frac{-4+9}{3}}{\frac{-2+3}{3}}=5y=\frac{6K+4}{K+1}=\frac{6\times \frac{-2}{3}+3}{\frac{-2}{3}+1}=\frac{-12+9}{\frac{3}{\frac{-2+3}{3}}}=-3\therefore (x,y)=(5,-3)$