Question

If point P (2,2) divides a line segment joining A (1,1) and B (5,5), then AP:PB = .

• A. 3 : 2
• B. 3 : 1
• C. 1 : 3

Answer 1

The correct option is C 1 : 3

Given, the points are
A (1,1) and B (5,5).

Also, the point that divides the line segment AB is P (2,2)
Let AP:PB = m : n.

Using section formula:
$x=\frac{m\times x_2+n\times x_1}{m+n}$
$2=\frac{m\times 5+n\times 1}{m+n}$
$\Rightarrow 2m+2n=5m+n$
$\Rightarrow n=3m$
$\Rightarrow \frac{n}{m}=\frac{3}{1}$
$or,m:n=1:3$