Question

If the point $(a,a)$ falls between the line $|x+y|=4$, then:

• A. $\left|a\right|=2$
• B. $\left|a\right|=3$
• C. $\left|a\right|<2$
• D. $\left|a\right|<3$

Answer 1

The correct option is C

$\left|a\right|<2$

Explanation for the correct option:

Identify the valid condition

Given lines,$x+y=4$ and $x+y=-4$

Since $(a,a)$ lies between these lines,

$\Rightarrow (a+a–4)(a+a+4)<0$

$\Rightarrow (2a–4)(2a+4)<0$

$\Rightarrow (a–2)(a+2)<0$

Thus, $-2<a<2$

So $\left|a\right|<2$

Hence, option (C) $\left|a\right|<2$, is the correct answer.