Question

If the point P(2,3) divides the line joining the points (5,6) and (8,9) then the ratio is

• A. 1:2 internally
• B. 1:2 externally
• C. 2:1 internally
• D. 2:1 externally

Answer 1

The correct option is B 1:2 externally

Let the ratio be $k:1$

Then, apply section formula

$\therefore \frac{k{x}_2+1\times x_1}{k+1}=2$, $\frac{k{y}_2+1\times y_1}{k+1}=3$

$\Rightarrow \frac{k+8+5}{k+1}=2$, $\frac{k\times 9+6}{k+1}=3$

$\Rightarrow \frac{9k+5}{k+1}=2$, $\frac{9k+6}{k+1}=3$

$\therefore \Rightarrow 8k+5=2k+2$

$\Rightarrow 6k=-3$

$\Rightarrow k=\frac{-3}{6}$

$\Rightarrow k=-\frac{1}{2}$

$\therefore$ Ratio$=1:2$

Externally due to ${}^{\prime }{-}^{\prime }$ sign.