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
• E. A rhombus which is not a square

Answer 1

Answer: (A)

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

Clearly, $ABCD$ is a square.