Question

P(2,6), Q(-4,1), a: b=1:2 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) = (2,6) 
Co-ordinates of the Point Q (x₂, y₂) = (-4,1)

Ration of division ( m₁:m₂) = 1 : 2

Now, Using the Section Formula, 

 P(x,y) = [(m₁x₂ + m₂x₁)/(m₁ + m₂) , (m₁y₂ + m₂y₁)/(m₁ + m₂)]
           = [(1 × -4 + 2 × 2)/(1 + 2) , (1 × 1 +  2 × 6 )/(1 + 2)]         
          = [0/3 , 13/3]
          = (0,13/3) 


Hence, the co-ordinates of the Point P is (0,13/3).


Hope it helps.

Answer 2

Given,

Coordinates of the Point P (x1, y1) =

(2,6)

Coordinates of the Point Q (X2, y2) =

(-4,1)

Ration of division ( m,:m2) = 1:2

Now, Using the Section Formula,

P(x.y) = [(m,x, + m2X,)/(m, + m2) , (m,y2 + = [(1 × -4 + 2 x 2)/(1+ 2), (1 x 1+ 2 =

məy;)/(m, + m2)1

x 6 )/(1 + 2)]

= [0/3, 13/3]

= (0,13/3) =

Hence, the co-ordinates of the Point P is (0,13/3).