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The line \( x+y=1 \) meets \( x \)-axis at \( A \) and \( y \)-axis at \( B, P \) is the mid-point of \( A B \)
\( P \) is the foot of die perpendicular from \( P \) to \( O A \);
\( M_{1} \) is that of \( P_{1} \) from \( O P \);
\( P_{2} \) is that of \( M_{1} \) from \( O A \)
\( M_{3} \) is that of \( P_{2} \) from \( O P \)
\( P_{3} \) is that of \( M_{2} \). from \( O A ; \) and so on.
If \( P_{n} \) denotes the \( n^{\text {th }} \), foot of the perpendicular on OA; then \( O P_{n} \) is
(a) \( \left(\frac{1}{2}\right)^{n-1} \)
(b) \( \left(\frac{1}{2}\right)^{n} \)
(c) \( \left(\frac{1}{2}\right)^{n+1} \)
(d) None of these
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