Question

If the sum of the distances of a point from two perpendicular lines is $5$, then its locus is

• A. a rectangle
• B. a square
• C. a straight line
• D. a circle

Answer 1

Answer: (B)

a square

Take the given two perpendicular lines as the coordinate axes, Let $P(x,y)$ be the point
Then the sum of the distances of P from given perpendicular lines is
$x+y$, if $x,y>0$
$-x+y$, if $x<0,y>0$
$-x-y$, if $x<0,y<0$ and $x-y$ if $x>0,y<0$
$\therefore \left|x\right|+\left|y\right|=5$ (constant)
$\therefore$ locus of P is the square ABCD.