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The locus of the mid-points of the perpendiculars drawn from points on the line, $x = 2y$ to the line $x = y$ is:
(1) $2x - 3y = 0$
(2) $5x - 7y = 0$
(3) $3x - 2y = 0$
(4) $7x - 5y = 0$
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