Explanation:
(C) : Given, \(|\mathrm{x}+\mathrm{y}|=4\)
So, the two lines are \(\mathrm{x}+\mathrm{y}=4\) and \(\mathrm{x}+\mathrm{y}=-4\) point (a, a) lies on the line \(y=x\)
And, Lines are parallel and points \((2,2)\) and \((-2,-2)\) lies on these lines.
So, the set of points \((a, a)\) between the lines \(x+y=4\) and \(x+y=-4\) is the portion of line \(y=x\) between lines \(\mathrm{x}+\mathrm{y}=4\) and \(\mathrm{x}+\mathrm{y}=-4\).
So, the line \(\mathrm{y}=\mathrm{x}\) and \(\mathrm{x}+\mathrm{y}=4\) intersect at the point (2, 2).
and line \(y=x\) and \(x+y=-4\) intersect at the point \((-2,-2)\)
So, the solution is the set of all points on the line \(y=x\) between point \((2,2)\) and \((-2,-2)\)
\(\therefore \quad-2\lt \mathrm{a}\lt 2\)
\(\therefore \quad|\mathrm{a}|\lt 2\)
