First slide

Equation of line in Straight lines

Question

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

Moderate

A

a square
B

a circle
C

a straight line
D

two intersecting lines

Solution

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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