ISI2016-DCG-16

Question

The set $\{(x,y)\: :\: \mid x\mid+\mid y\mid\:\leq\:1\}$ is represented by the shaded region in

 

• A.
• B.
• C.
• D.

 

Answer 1

The corresponding set represents all the points in the area inside and on the figure created by intersection of all these lines:

(1)  $x + y = 1$ => $ y = -x +1$ => Straight line passing through $(1, 0)$ and $(0, 1)$

(2)  $x - y = 1$ => $ y = x -1$ => Straight line passing through $(1, 0)$ and $(0, -1)$

(3)  $-x + y = 1$ => $ y = x +1$ => Straight line passing through $(-1, 0)$ and $(0, 1)$

(4)  $-x - y = 1$ => $ y = -x -1$ => Straight line passing through $(-1, 0)$ and $(0, -1)$

 

Option (D) is the correct answer.