Question

If the sum of the distance of a moving point from 2 perp. lines in a plane is always 1 then its locus is?

Answer 1

Hey.

Here is the answer.

Let the perpendiculars lines be the x – axis and y – axis.  The sum of the distances from the the point P (x, y) is 1. ie.

|x| + |y| = 1  – this is the locus of the point P which would be the rhombus whose sides are 

x + y = 1; –x + y = 1; x – y = 1; –x – y = 1

If the perpendicular lines are other than co-ordinate axes, then we can get the same solution by using the transformation of the axes concept.

So, rhombus or can say square is the answer .

Thanks.