The image of P(a,b) along y=x is Q(b,a). Translating it 2 units along the positive direction of X-axis, it becomes R(b+2,a). Then, rotation through ‌
Ï€
4
about the origin in the anticlockwise direction, the final position of the point P is (−‌
⇒b−a=−3‌‌‌⋅⋅⋅⋅⋅⋅⋅(i) ‌ and ‌‌‌
a+b+2
√2
=‌
7
√2
⇒‌‌a+b=5‌‌‌⋅⋅⋅⋅⋅⋅⋅(ii) Adding Eqs. (i) and (ii), 2b=2⇒b=1 Substitute the value of b in Eq. (ii), a=4 Now, ‌‌2a+b=2×4+1=9