ISI2014-DCG-28

Question

The area enclosed by the curve $\mid\: x \mid + \mid y \mid =1$ is

• A. $1$
• B. $2$
• C. $\sqrt{2}$
• D. $4$

Answer 1

Answer: $B.$ $2$

$x+y=1$. when$ x>0 $ and$ y>0$

$-x+y=1$ when $x<0$ and $y>40$

$-x-y=1$ when both $x$ and $y$ are $<0$

$x-y=1$ when $x>0$ and $y<0$

Now, on plotting these equations,

The obtained coordinates would be:

$(1,0) (0,1) (-1,0) (0,-1)$

On joining these co-ordinates, a square of side $\sqrt2$ units would be obtained.

Therefore, area enclosed $= $ Area of square $=(\sqrt2)^2 = 2$ units

Therefore, option $B$ is the right answer.

Answer 2

Sorry for the bad handwriting!