Maths · Distance formula, sections formula, locus and its equation
Mid point \) and \) is and mid point of and is and so on. Coordinates of are:
Mid point \( \boldsymbol{A}(\mathbf{0}, \mathbf{0}) \) and \( \boldsymbol{B}(\mathbf{1 0 2 4}, \mathbf{2 0 4 8}) \) is \( A_{1} \) and mid point of \( A_{1} \) and \( B \) is \( A_{2} \) and so on. Coordinates of \( \boldsymbol{A}_{\mathbf{1 0}} \) are:
- A. (1022,2044) ) (1022,2444)
- B. (1025,2050)
- C. (1023,2046)
- D. (1,2)
Step-by-step solution
Starting from A₀ = (0,0) and B = (1024,2048), each Aₙ is the midpoint of Aₙ₋₁ and B. This gives recurrence xₙ = (xₙ₋₁ + 1024)/2 and yₙ = (yₙ₋₁ + 2048)/2. Solving: xₙ = 1024(1 - 1/2ⁿ), yₙ = 2048(1 - 1/2ⁿ). For n=10, x₁₀ = 1024(1 - 1/1024) = 1023, y₁₀ = 2048(1 - 1/1024) = 2046.
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