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in Mathematics by (53.3k points)

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. 

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Best answer

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.

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