Question

If the point (a, a) lies between the lines |x + y| = 2, then which one of the following is correct?

• A. $|a|<2$
• B. $|a|<\sqrt{2}$
• C. $|a|<1$
• D. $|a|<\frac{1}{\sqrt{2}}$

Answer 1

The correct option is C $|a|<1$

$|x+y|=2$

So, the two lines are $x+y=2$ and $x+y=-2$

Point $(a,a)$ lies on the line $y=x$

So, the set of points $(a,a)$ between the lines $x+y=2$ and $x+y=-2$ is the portion of line $y=x$ between lines $x+y=2$ and $x+y=-2$

The line $y=x$ and $x+y=2$ intersect at the point $(1,1)$

and The line $y=x$ and $x+y=-2$ intersect at the point $(-1,-1)$

So, the solution is the set of all points on the line $y=x$ between points $(1,1)$

and $(-1,-1)$

$\therefore -1<a<1$

$\therefore |a|<1$

The answer is option (C)