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  • If the sum of the distances of a point from two perpendicular lines in a plane is 1 , then its locus is  Option: 1 a square

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

Option: 1

a square


 


Option: 2

a circle
 


Option: 3

a straight line
 


Option: 4

two intersecting lines


Answers (1)

best_answer

Let the two perpendicular lines be taken as the co-ordinate axes. If \mathrm{P}(\mathrm{x}, \mathrm{y}) is a point in the plane, such that the sum of distances of \mathrm{P} from the axes is equal to 1 , then \mathrm{|x|+|y|=1}

\mathrm{ \Rightarrow \mathrm{x}+\mathrm{y}=1, \mathrm{x}-\mathrm{y}=1,-\mathrm{x}+\mathrm{y}=1,-\mathrm{x}-\mathrm{y}=1 }

These four lines form a square.

Hence locus of the point \mathrm{ P } is a square.

Hence option 1 is correct.

Posted by

Rishabh

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