The point $P\left(a,b\right)$ undergoes the following three transformations successively:
$\left(a\right)$ reflection about the line $y=x.$
$\left(b\right)$ translation through $2$ units along the positive direction of $x-$ axis.
$\left(c\right)$ rotation through angle $\frac{\pi }{4}$ about the origin in the anti-clockwise direction.

If the co-ordinates of the final position of the point $P$ are $\left(-\frac{1}{\sqrt{2}},\frac{7}{\sqrt{2}}\right)$, then the value of $2a+b$ is equal to:

• A

  $13$
• Correct answer
  B

  $9$
• C

  $5$
• D

  $7$

Hence, the correct answer is option: 'B'.