Question

The midpoint of the line joining the points $(-10,8)$ and $(-6,12)$ divides the line joining the points $(4,-2)$ and $(-2,4)$ in the ratio

• A. $1:2$ internally
• B. $1:2$ externally
• C. $2:1$ internally
• D. $2:1$ externally
• E. $2:3$ externally

Answer 1

Answer: (D)

The midpoint of the line joining the points $(-10,8)$ and $(-6,12)$ is $\left(\frac{-10-6}{2},\frac{8+12}{2}\right)$ ie, $(-8,10)$ . Let $(-8,10)$ divides the line joining the points $(4,-2)$ and $(-2,4)$ in the ratio $m:n$ .
$\therefore$ $\frac{m(-2)+n(4)}{m+n}=-8$
$\Rightarrow$ $-2m+4n=-8m-8n$
$\Rightarrow$ $6m=-12n$
$\Rightarrow$ $\frac{m}{n}=\frac{-2}{1}$
$\therefore$ $(-8,10)$ divides the line joining the points $(4,-2)$ and $(-2,4)$ in the ratio $2:1$ externally.