Question

If the sum of the distances of a point from two perpendicular lines in a plane is 1, then prove that its locus is a square.

Answer 1

Take the two perpendicular lines as coordinate axes. P(x, y) is a point on the locus ⇔|x| + |y| = 1. This implies that

x + y = 1

x - y = 1

-x + y = 1

-x - y = 1

These lines form a square.