Question

Find the ratio in which the point P(1, 2) divides the line joining the points A(-2, 1) and B(7, 4).

• A. 1:2
• B. 2:3
• C. 3:4
• D. 1:3

Answer 1

The correct option is A 1:2

Plotting the given points on graph paper we get:

By subtracting the cooresponding corrdinates we get:
AX = 1 - ( - 2) = 3
PX = 2 - 1 = 1

AY = 7 - (-2) = 9
BY = 4 - 1 = 3

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

$\frac{AP}{AB}=\frac{3}{9}$

$\frac{AP}{AB}=\frac{1}{3}$

$\frac{AP}{AP+PB}=\frac{1}{3}$

Reducing the above equation we get:
$\frac{AP}{PB}=\frac{1}{2}$

$\therefore$ The ratio in which 'P' divides AB is 1 : 2