Question

If 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

Answer 1

Answer: (A)

a square

Let the two perpendicular lines be taken as the coordinate axes. If $(h,k)$ be any point on the locus, then according to the given condition $|h|+|k|=1$ .
Hence, the locus of $(h,k)$ is $|x|+|y|=1$
Now the four lines are
$x+y=1$for first quadrant.
$-x+y=1$for second quadrant.
$-x-y=1$ for third quadrant.
$x-y=1$ for fourth quadrant .
These lines are perpendicular to each other and diagonals are equal . therefore they form a square.