A variable line whose slope is \( -2 \) cuts the \( x \) and \( y \...

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A variable line whose slope is \( -2 \) cuts the \( x \) and \( y \) axes respectively at points \( A \) and \( C \). A rhombus \( A B C D \) is completed such that vertex \( B \) lies on the line \( y=x \). Then the locus of vertex \( D \) is
\( \mathrm{P} \)
(A) \( 2 x+y=1 \)
(B) \( x-y=0 \)
(C) \( x+y=0 \)
(D) \( x+2 y=0 \)
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