Question

The ratio in which the point $(2,y)$ divides the line segment joining $(4,3)$ and $(6,3)$ is

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

Answer 1

The correct option is A $1:2$ externally

Let $A\equiv (4,3),B\equiv (6,3)$ and $P\equiv (2,y)$

Assuming $P$ divides $AB$ internally in the ratio $m:n$, then
$2=\frac{6m+4n}{m+n}\Rightarrow 2m+2n=6m+4n\therefore \frac{m}{n}=-\frac{1}{2}$
Since $m:n$ is negative, therefore division is external i.e., $P$ divides $AB$ externally in the ratio $1:2.$