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The locus of the mid - points of the perpendiculars drawn from points on the line, x = 2 y to the line x = y  is:

Option 1 -

7 x - 5 y = 0

Option 2 -

3 x - 2 y = 0

Option 3 -

2 x - 3 y = 0

Option 4 -

5 x - 7 y = 0

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