Question

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

Answer 1

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

Also, the point that divides the line segment AB is P (2,2)

By subtracting the cooresponding corrdinates we get:
AX = 2 - (1) = 1
PX = 2 - 1 = 1

AY = 5 - (1) = 4
BY = 5 - 1 = 4

We know that trinagle APX is similar to triangle ABY by AA rule.
$\frac{AP}{AB}=\frac{AX}{AY}$

$\frac{AP}{AB}=\frac{1}{4}$

Reducing the above equation we get:
$\frac{AP}{PB}=\frac{1}{3}$

$\therefore$ The ratio in which 'P' divides AB is 1 : 3