1.

Given A(4,-3), B(8,5). Find the coordinates of the point that divides segment AB in the ratio 3ः1.

Answer» Given, 
Co-ordinates of the Point A (x₁, y₁) = (4,-3) 
Co-ordinates of the Point B (x₂, y₂) = (8,5)

Ration of division ( m₁:m₂) = 3 : 1

Now, USING the Section FORMULA, 

 P(x,y) = [(m₁x₂ + m₂x₁)/(m₁ + m₂) , (m₁y₂ + m₂y₁)/(m₁ + m₂)]
           = [(3 × 8 + 1 × 4)/(3 + 1) , (3 × 5 + 1 × -3)/(3 + 1)]
           = [28/4 , 12/4]
          = (7,3) 


Hence, the co-ordinates of the Point P is (7,3).


Hope it helps.


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