JEE MATHEMATICS MCQ: 2D GEOMETRY SYSTEM

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Application +4 | -1

Let

A(a, b)

be a fixed point and

O

be the origin of coordinates. If

A_1

is the mid-point of

O A, A_2

is the mid-point of

A A_1, A_3

is the mid-point of

A A_2

and so on. Then the coordinates of

A_n

are

View answer and explanation

Correct option: A

\left(a\left(1-2^{-n}\right), b\left(1-2^{-n}\right)\right)

Option A (a(1-2⁻ⁿ), b(1-2⁻ⁿ)) is correct because the coordinates of Aₙ converge to (a, b) as n approaches infinity, and the given expression reflects this convergence.

JEE MATHEMATICS MCQ: 2D GEOMETRY SYSTEM

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