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

square
B

circle
C

straight line
D

two intersecting lines

Solution

Let the two perpendicular lines be the coordinate axes.
Let (x, y) be the point, sum of whose distances from two axes is1.
Then we must have
$\begin{aligned} | x | + | y | = 1 \\ or \pm x \pm y = 1 \end{aligned}$
The four lines are $x + y = 1, x - y = 1, - x + y = 1, - x - y = 1$
Any two adjacent sides are perpendicular to each other. Also, each line is equidistant from the origin.
Therefore, the figure formed is a square.

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