P(-3,7), Q(1,-4), a:b=2:1 find the co-ordinates of point A which divides segment PQ in the ratio a:b.
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32
Given,
Co-ordinates of the Point P (x₁, y₁) = (-3,7)
Co-ordinates of the Point Q (x₂, y₂) = (1,-4)
Ration of division ( m₁:m₂) = 2 : 1
Now, Using the Section Formula,
A(x,y) = [(m₁x₂ + m₂x₁)/(m₁ + m₂) , (m₁y₂ + m₂y₁)/(m₁ + m₂)]
= [( 2 × 1 + 1 × -3 )/(2 + 1) , (2 × -4 + 1 × 7 )/(2 + 1)]
= [-1/3 , -1/3]
= (-1/3,-1/3)
Hence, the co-ordinates of the Point A is (-1/3,-1/3).
Hope it helps.
Co-ordinates of the Point P (x₁, y₁) = (-3,7)
Co-ordinates of the Point Q (x₂, y₂) = (1,-4)
Ration of division ( m₁:m₂) = 2 : 1
Now, Using the Section Formula,
A(x,y) = [(m₁x₂ + m₂x₁)/(m₁ + m₂) , (m₁y₂ + m₂y₁)/(m₁ + m₂)]
= [( 2 × 1 + 1 × -3 )/(2 + 1) , (2 × -4 + 1 × 7 )/(2 + 1)]
= [-1/3 , -1/3]
= (-1/3,-1/3)
Hence, the co-ordinates of the Point A is (-1/3,-1/3).
Hope it helps.
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