Question

A(9,20) and B(15,5) are two end points of a line segment divided by a point P(11,15). Find the ratio in which the point P divides the line segment AB.

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

Answer 1

The correct option is C 1 : 2

Suppose, point P(11, 15) divides segment AB in the ratio $m:n$.
By Section formula, $x=\frac{m{x}_2+n{x}_1}{m+n}$
$\Rightarrow 11=\frac{15m+9n}{m+n}$
$\Rightarrow 11m+11n=15m+9n$
$\Rightarrow 4m=2n$
$\therefore \frac{m}{n}=\frac{2}{4}=\frac{1}{2}$

Hence, the ratio in which (11, 15) divides AB is 1 : 2.