If the sum of the distances of a point f...

If the sum of the distances of a point from two perpendicular lines in a plane is 1, then its locus is(A) a square (b) a circle (C) a straight line (d) two intersecting lines

a square

a circle

a straight line

two intersecting lines

Text Solution

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Let the two perpendicular lines be taken as the coordinates axes. If (h,k) is any point on the locus, then according to the given condition, |h|+|k|=1. Hence, the locus of (h,k) is |x|+|y|=1. This consists of four line segments enclosing a square as shown in the figure.

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