The point \( P(a, b) \) undergoes the following three transformations successively:
(a) Reflection about the line \( y = x \)
(b) Translation through \( 2 \) units along the positive direction of x-axis
(c) Rotation through angle \( \dfrac{\pi}{4} \) about the origin in the anti-clockwise direction
If the co-ordinates of the final position of the point \( P \) are \( \left( -\dfrac{1}{\sqrt{2}}, \dfrac{7}{\sqrt{2}} \right) \), then the value of \( 2a + b \) is equal to:
