The locus of mid points of the perpendiculars drawn from points on the line to the line is
Explanation for the correct answer
Locus of midpoint :
Let be the perpendicular drawn from the line to the line
is the midnight of .
The equation of the line can be written as
intersects at [ is the midnight of ]
intersects at
Midpoint formula for points is
Using midpoint formula for , and is
By making an equation with points
So, the locus of is
Hence, option C is correct.