Question

The set $\\{(x, y) : x + y =1\\}$ in the $xy$ plane represents

• A. a square
• B. A circle
• C. An ellipse
• D. A rectangle which is not a square

Answer 1

Answer: (A)

a square

Answer 2

We have,
$|x|+|y|=1=\begin{cases}x +y=1, & x, y \in \text { I quadrant } \\\ -x+ y=1, & x, y \in \text { II quadrant } \\\ -x -y=1, & x, y \in \text { III quadrant } \\\ x-y=1, & x, y \in \text { IV quadrant }\end{cases}$

Clearly, $A B C D$ is a square.