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The line \( \mathrm{AB} \) whose equation is \( x-y=2 \) cuts the \( x \)-axis at \( A \) and \( B \) is \( (4,2) \). The line \( A B \) is rotated about \( A \) through \( 45^{\circ} \) in the anticlockwise direction. Find the new position of \( B \) and the equation of the line \( \mathrm{AB} \) in the new position.

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