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

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

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Solution:

$\frac{\alpha-\beta}{2\alpha-\beta}=-1$
$3\alpha=2\beta$
$h=\frac{2\alpha+\beta}{2}$
$2h=\frac{7\alpha}{2}$
$k=\frac{\alpha+\beta}{2}$
$2k=\frac{5\alpha}{2}$
$\frac{h}{k}=\frac{7}{5}$
$5x=7y$

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