If the sum of the distances of a point from two perpendicular lines in a plane is 1 , then its locus is
If the sum of the distances of a point from two perpendicular lines in a plane is 1 , then its locus is
Two intersecting lines
Square
A straight line
Circle
Solution
Let $P=(h, k)$ be any point in the locus let $x, y$-axes be two perpendicular lines
$\therefore$ Distance from $P(h, k)$ to $X$-axis $=1$ (given)
$
|k|=1
$
Distance from $P(h, k)$ to $Y$-axis $=1 \Rightarrow|h|=1$
According to the question, $|h|+|k|=1$
$\therefore$ The locus of point $(h, k)$ is $|x|+|y|=1$
$\therefore$ It is a square
Hence, option (2) is correct