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Option (i) (a(1-2⁻ⁿ) , b(1-2⁻ⁿ))
Step-by-step explanation:
Given: The co-ordinates of point A are (a,b) and O is the origin. Also, mid-point of OA is A₁, mid-point of AA₁ is A₂ and so on upto Aₙ.
w.k.t., mid-point of line joining two-point P(x₁,y₁) and Q(x₂,y₂) is
So, co-ordinates of point A₁ =
Similarly, co-ordinates of point A₂ =
And, co-ordinates of point A₃ =
Also, co-ordinates of point A₄ =
By observing the above four points and the given options, we can write the general co-ordinates of mid point.
So, the co-ordinates of point Aₙ are (a(1-2⁻ⁿ) , b(1-2⁻ⁿ)).
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