First slide

Cartesian plane

Question

If the distance of any point ( x, y) from the origin is defined as d (x, y) = max {I x I, I y I} , then the locus of the point (x, y), where d (x, y) =1, is

Moderate

A

a circle
B

a square
C

a triangle
D

none of these

Solution

We have,
$d (x, y) = 1$
$\begin{array}{l} \Rightarrow max {| x |, | y |} = 1 \\ \Rightarrow | x | \leq 1 and | y | \leq 1 \\ \Rightarrow - 1 \leq x \leq 1 and - 1 \leq y \leq 1 \end{array}$
Locus of $(x, y)$ is the square having its vertices at
(1, 1), (-1, 1), (-1, -1) and (1, -1).

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