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

Question

The locus of the mid-points of the perpendiculars drawn from points on the line, x=2y to the line x = y is : (A) 2x - 3y=0 (B) 3x - 2y=0 (C) 5x - 7y=0 (D) 7x - 5y=0

Tardigrade Admin · Accepted Answer

(α-β/2α-β)=-1 3α=2β h=(2α+β/2) 2h=(7α/2) k=(α+β/2) 2k=(5α/2) (h/k)=(7/5) 5x=7y

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

$2 x - 3 y = 0$

$3 x - 2 y = 0$

$5 x - 7 y = 0$

$7 x - 5 y = 0$

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

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

2x−3y=0

3x−2y=0

5x−7y=0

7x−5y=0