(A) Let the two perpendicular lines be the coordinate axes $x = 0$ and $y = 0$. Let the point $P$ be $(x, y)$. The distance of $P$ from $x = 0$ is $|x

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(A) Let the two perpendicular lines be the coordinate axes $x = 0$ and $y = 0$. Let the point $P$ be $(x, y)$. The distance of $P$ from $x = 0$ is $|x|$ and from $y = 0$ is $|y|$. Given that the sum of the distances is $1$,we have $|x| + |y| = 1$. This equation represents a square with vertices at $(1, 0), (0, 1), (-1, 0),$ and $(0, -1)$. $A$ square is a special type of rhombus. Therefore,the locus of $P$ is a rhombus.

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

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rhombus
B
circle
C
straight line
D
pair of straight lines

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

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