Question

A(3,10) and B(8,15) are two end points of a line segment divided by a point P(4,5). Find the ratio in which the point P divides the line segment AB.

• A. 2 : 3
• B. 4 : 3
• C. 3 : 4
• D. 1 : 4

Answer 1

The correct option is D 1 : 4

Suppose, point P(4,5) divides segment AB in the ratio $m:n$.
By Section formula, $x=\frac{m{x}_2+n{x}_1}{m+n}$
$\Rightarrow 4=\frac{8m+3n}{m+n}$
$\Rightarrow 4m+4n=8m+3n$
$\Rightarrow 4m=n$
$\Rightarrow \frac{m}{n}=\frac{1}{4}$
Hence, the ratio in which (4,5) divides AB is 1 : 4.