Straight Lines and Pair of Straight Lines

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 ${\pi \over 4}$ about the origin in the anti-clockwise direction. If the co-ordinates of the final position of the point P are $\left( { - {1 \over {\sqrt 2 }},{7 \over {\sqrt 2 }}} \right)$, then the value of 2a + b is equal to :