Question

Find the ratio in which (11,15) divides the line segment joining the points (15,5) and (9,20)

Answer 1

Let the ratio be k:1 
Now by section formula, 
kx2+1*x1/k+1=11 
k*9+1*15/k+1=11 
11k+11=9k+15 
2k=4 
k=2 

Answer 2

Hi !

We have to apply section formula to find the answer .

Let the point P(11,15) divide the line segment AB in the ratio m₁:m₂
A = (15,5) ==> x₁ = 15 , y₁ = 5
A = (9,20)  ==> x₂ = 9 , y₂ = 20

P = (11,15) ==> x = 11 , y = 15

Here is the formula :-

x = $\frac{ m_{1} x_{2} + m _{2}x_{1} }{m_{1}+ m _{2} }$

11 = $\frac{ 9m_{1} + 15m _{2} }{m_{1}+ m _{2} }$

11(m₁ + m₂) = 9m₁ + 15m₂
11m₁ + 11m₂ =  9m₁ + 15m₂
2m₁ = 4m₂
m₁/m₂ = 4/2
m₁/m₂ = 2/1

The ratio is 2:1