Question

P(-2,-5), Q(4,3), a:b=3:4 find the co-ordinates of point A which divides segment PQ in the ratio a:b.

Answer 1

Given, 
Co-ordinates of the Point P (x₁, y₁) = (-2,-5) 
Co-ordinates of the Point Q (x₂, y₂) = (4, 3)

Ration of division ( m₁:m₂) = 3 : 4

Now, Using the Section Formula, 

 A(x,y) = [(m₁x₂ + m₂x₁)/(m₁ + m₂) , (m₁y₂ + m₂y₁)/(m₁ + m₂)]
           = [( 3 × 4 + 4 × -2 )/(3 + 4) , (3 × 3 + 4 × -5 )/(3 + 4)]          
          = [4/7 , -11/7]
          = (4/7,-11/7) 


Hence, the co-ordinates of the Point A is (4/7, -11/7).


Hope it helps.